What is $sum_r=0^(p-1)/2binomfracp-12r^2cdot a^2r mod p$ ?, where a is any non zero integer. The 2019 Stack Overflow Developer Survey Results Are In Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)$(1+x+x^2)^n = sum_r=0^2na_rcdot x^r$ and $sum_r=0^n(-1)^rcdot a_rcdot binomnr = kcdot binomnfracn3$. Then $k=$Prove $sum_k=0^nfracbinomnk(-1)^kk+1$ = $frac1n+1$What is a closed form for $sum_r=1^k binom nr$, where $kleqslant n$.What is $sum_r=0^n frac(-1)^rbinomnr$?Upper bound for $fracsum_i=0^k binomn-2isum_i=0^k binomni$Evaluating $sum_k=0^nfrac1k+1binom2kkbinomnk$What is $sum_m=0,2,cdots,nbinomfracm+n2m $?prove that $sum_k=0^n frac1k+1binom2kkbinom2n-2kn-k=binom2n+1n$Combinatorial interpretation of coefficient $b_n$ in $B(x) = A_1(x) cdot cdot cdot A_r(x) = sum_n=0^infty fracb_nn! x^n$Calculate $sum_i=0^ni^2 cdot binomni^2 $
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What is $sum_r=0^(p-1)/2binomfracp-12r^2cdot a^2r mod p$ ?, where a is any non zero integer.
The 2019 Stack Overflow Developer Survey Results Are In
Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)$(1+x+x^2)^n = sum_r=0^2na_rcdot x^r$ and $sum_r=0^n(-1)^rcdot a_rcdot binomnr = kcdot binomnfracn3$. Then $k=$Prove $sum_k=0^nfracbinomnk(-1)^kk+1$ = $frac1n+1$What is a closed form for $sum_r=1^k binom nr$, where $kleqslant n$.What is $sum_r=0^n frac(-1)^rbinomnr$?Upper bound for $fracsum_i=0^k binomn-2isum_i=0^k binomni$Evaluating $sum_k=0^nfrac1k+1binom2kkbinomnk$What is $sum_m=0,2,cdots,nbinomfracm+n2m $?prove that $sum_k=0^n frac1k+1binom2kkbinom2n-2kn-k=binom2n+1n$Combinatorial interpretation of coefficient $b_n$ in $B(x) = A_1(x) cdot cdot cdot A_r(x) = sum_n=0^infty fracb_nn! x^n$Calculate $sum_i=0^ni^2 cdot binomni^2 $
$begingroup$
I have tried to compare the coefficient of $x^n$ in $((1+x)(x+a^2))^n$.
combinatorics
asked Apr 8 at 6:06
Nilanjan BagNilanjan Bag
42
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Nilanjan Bag is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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$endgroup$
add a comment |
$begingroup$
I have tried to compare the coefficient of $x^n$ in $((1+x)(x+a^2))^n$.
combinatorics
asked Apr 8 at 6:06
Nilanjan BagNilanjan Bag
42
New contributor
Nilanjan Bag is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
$begingroup$
When $r=p-1$ it's more than $(p-1)/2.$ What does the binomial coefficient mean in this case? [If zero suggest limits of sum adjusted.]
$endgroup$
– coffeemath
Apr 8 at 6:19
$begingroup$
you are right. it is a typo. It should be (p-1)/2. I have corrected it.
$endgroup$
– Nilanjan Bag
Apr 8 at 8:36
add a comment |
$begingroup$
I have tried to compare the coefficient of $x^n$ in $((1+x)(x+a^2))^n$.
combinatorics
asked Apr 8 at 6:06
Nilanjan BagNilanjan Bag
42
New contributor
Nilanjan Bag is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
I have tried to compare the coefficient of $x^n$ in $((1+x)(x+a^2))^n$.
combinatorics
combinatorics
asked Apr 8 at 6:06
Nilanjan BagNilanjan Bag
42
New contributor
Nilanjan Bag is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Apr 8 at 6:06
Nilanjan BagNilanjan Bag
42
New contributor
Nilanjan Bag is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited Apr 8 at 8:36
Nilanjan Bag
asked Apr 8 at 6:06
Nilanjan BagNilanjan Bag
42
New contributor
Nilanjan Bag is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Apr 8 at 6:06
Nilanjan BagNilanjan Bag
42
asked Apr 8 at 6:06
Nilanjan BagNilanjan Bag
42
42
New contributor
Nilanjan Bag is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Nilanjan Bag is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Nilanjan Bag is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$begingroup$
When $r=p-1$ it's more than $(p-1)/2.$ What does the binomial coefficient mean in this case? [If zero suggest limits of sum adjusted.]
$endgroup$
– coffeemath
Apr 8 at 6:19
$begingroup$
you are right. it is a typo. It should be (p-1)/2. I have corrected it.
$endgroup$
– Nilanjan Bag
Apr 8 at 8:36
add a comment |
$begingroup$
When $r=p-1$ it's more than $(p-1)/2.$ What does the binomial coefficient mean in this case? [If zero suggest limits of sum adjusted.]
$endgroup$
– coffeemath
Apr 8 at 6:19
$begingroup$
you are right. it is a typo. It should be (p-1)/2. I have corrected it.
$endgroup$
– Nilanjan Bag
Apr 8 at 8:36
$begingroup$
When $r=p-1$ it's more than $(p-1)/2.$ What does the binomial coefficient mean in this case? [If zero suggest limits of sum adjusted.]
$endgroup$
– coffeemath
Apr 8 at 6:19
$begingroup$
When $r=p-1$ it's more than $(p-1)/2.$ What does the binomial coefficient mean in this case? [If zero suggest limits of sum adjusted.]
$endgroup$
– coffeemath
Apr 8 at 6:19
$begingroup$
you are right. it is a typo. It should be (p-1)/2. I have corrected it.
$endgroup$
– Nilanjan Bag
Apr 8 at 8:36
$begingroup$
you are right. it is a typo. It should be (p-1)/2. I have corrected it.
$endgroup$
– Nilanjan Bag
Apr 8 at 8:36
add a comment |
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$begingroup$
When $r=p-1$ it's more than $(p-1)/2.$ What does the binomial coefficient mean in this case? [If zero suggest limits of sum adjusted.]
$endgroup$
– coffeemath
Apr 8 at 6:19
$begingroup$
you are right. it is a typo. It should be (p-1)/2. I have corrected it.
$endgroup$
– Nilanjan Bag
Apr 8 at 8:36