A340863 a(n) = n!*LaguerreL(n, -n^2).
1, 2, 34, 1626, 151064, 23046370, 5228520912, 1651548277946, 692979602529664, 372856154213080674, 250277853396112428800, 205025892171407329263802, 201314381459222197472984064, 233396220344077025321595074306
Offset: 0
Keywords
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..214
- Eric Weisstein's World of Mathematics, Laguerre Polynomial
- Wikipedia, Laguerre polynomials
- Index entries for sequences related to Laguerre polynomials
Programs
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Mathematica
Table[n! * LaguerreL[n, -n^2], {n, 0, 13}] (* Amiram Eldar, Feb 05 2021 *) -
PARI
a(n) = sum(k=0, n, n^(2*k)*(n-k)!*binomial(n, k)^2);
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PARI
a(n) = n!*pollaguerre(n, 0, -n^2); \\ Michel Marcus, Feb 05 2021
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