|
%I #32 Feb 14 2021 08:38:18
%S 1,2,34,1626,151064,23046370,5228520912,1651548277946,692979602529664,
%T 372856154213080674,250277853396112428800,205025892171407329263802,
%U 201314381459222197472984064,233396220344077025321595074306
%N a(n) = n!*LaguerreL(n, -n^2).
%H Seiichi Manyama, <a href="/A340863/b340863.txt">Table of n, a(n) for n = 0..214</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LaguerrePolynomial.html">Laguerre Polynomial</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Laguerre_polynomials">Laguerre polynomials</a>
%H <a href="/index/La#Laguerre">Index entries for sequences related to Laguerre polynomials</a>
%F a(n) = Sum_{k=0..n} n^(2*k) * (n-k)! * binomial(n,k)^2.
%F a(n) = n! * [x^n] exp(n^2 * x/(1-x))/(1-x).
%F a(n) = A289192(n,n^2).
%F a(n) ~ exp(1) * n^(2*n). - _Vaclav Kotesovec_, Feb 14 2021
%t Table[n! * LaguerreL[n, -n^2], {n, 0, 13}] (* _Amiram Eldar_, Feb 05 2021 *)
%o (PARI) a(n) = sum(k=0, n, n^(2*k)*(n-k)!*binomial(n, k)^2);
%o (PARI) a(n) = n!*pollaguerre(n, 0, -n^2); \\ _Michel Marcus_, Feb 05 2021
%Y Main diagonal of A338435.
%Y Cf. A277373, A289192.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Feb 05 2021
| 