A183609 a(n) = Sum_{k=0..n-1} binomial(n^2+k^2, k) * (n-k)^2/(n^2 + k^2) for n>0 with a(0)=1.

1, 1, 2, 11, 140, 3317, 121528, 6119023, 393990922, 30967643569, 2877662229666, 308859441395270, 37617620420277248, 5127547379787329620, 773519559519251515487, 127966383690518560215307, 23038617512398942817456756

Offset

0,3

Links

Table of n, a(n) for n=0..16.

Formula

a(n) ~ 2^(n-5/2) * exp(n-5/4) * n^(n-7/2) / sqrt(Pi). - Vaclav Kotesovec, Mar 06 2014

Mathematica

Flatten[{1, Table[Sum[Binomial[n^2+k^2, k]*(n-k)^2/(n^2+k^2), {k, 0, n-1}], {n, 1, 20}]}] (* Vaclav Kotesovec, Mar 06 2014 *)

Prog

(PARI) {a(n)=if(n<0, 0, 0^n+sum(k=0, n-1, binomial(n^2+k^2, k)*(n-k)^2/(n^2+k^2)))}

Crossrefs

Sequence in context: A365357 A295811 A177753 * A113148 A377894 A193209

Adjacent sequences: A183606 A183607 A183608 * A183610 A183611 A183612

Keyword

nonn

Author

Paul D. Hanna, Jan 15 2011

Status

approved