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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 (list; graph; refs; listen; history; text; internal format)
 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 Main diagonal of A338435. Cf. A277373, A289192. Sequence in context: A215957 A171732 A291903 * A198977 A198718 A198909 Adjacent sequences:  A340860 A340861 A340862 * A340864 A340865 A340866 KEYWORD nonn AUTHOR Seiichi Manyama, Feb 05 2021 STATUS approved

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Last modified June 16 21:55 EDT 2021. Contains 345080 sequences. (Running on oeis4.)