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A340863
a(n) = n!*LaguerreL(n, -n^2).
2
1, 2, 34, 1626, 151064, 23046370, 5228520912, 1651548277946, 692979602529664, 372856154213080674, 250277853396112428800, 205025892171407329263802, 201314381459222197472984064, 233396220344077025321595074306
OFFSET
0,2
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
Main diagonal of A338435.
Sequence in context: A215957 A171732 A291903 * A198977 A198718 A198909
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Feb 05 2021
STATUS
approved