OFFSET
0,2
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..214
Eric Weisstein's World of Mathematics, Laguerre Polynomial
Wikipedia, Laguerre polynomials
FORMULA
a(n) = Sum_{k=0..n} n^(2*k) * (n-k)! * binomial(n,k)^2.
a(n) = n! * [x^n] exp(n^2 * x/(1-x))/(1-x).
a(n) = A289192(n,n^2).
a(n) ~ exp(1) * n^(2*n). - Vaclav Kotesovec, Feb 14 2021
MATHEMATICA
Table[n! * LaguerreL[n, -n^2], {n, 0, 13}] (* Amiram Eldar, Feb 05 2021 *)
PROG
(PARI) a(n) = sum(k=0, n, n^(2*k)*(n-k)!*binomial(n, k)^2);
(PARI) a(n) = n!*pollaguerre(n, 0, -n^2); \\ Michel Marcus, Feb 05 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Feb 05 2021
STATUS
approved