A295418 a(n) = n! * Laguerre(n, n*(n-1), -n).

1, 2, 32, 1422, 124832, 18246850, 4005713952, 1232956594814, 506672220394496, 267992015325604578, 177340024595660672000, 143531889358151618790862, 139482579412432078779322368, 160267575964062522718064075618, 214924620455826226723051817295872

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..213

Eric Weisstein's World of Mathematics, Laguerre Polynomial

Wikipedia, Laguerre polynomials

Index entries for sequences related to Laguerre polynomials

Formula

a(n) = n! * Sum_{k=0..n} binomial(n^2,n-k)*n^k/k!.

a(n) ~ exp(1/2) * n^(2*n).

a(n) = n! * [x^n] exp(n*x/(1 - x))/(1 - x)^(n^2-n+1). - Ilya Gutkovskiy, Nov 23 2017

Mathematica

Table[n!*LaguerreL[n, n*(n-1), -n], {n, 0, 15}]
Join[{1}, Table[n!*Sum[Binomial[n^2, n-k]*n^k/k!, {k, 0, n}], {n, 1, 15}]]

Prog

(PARI) for(n=0, 25, print1(n!*sum(k=0, n, binomial(n^2, n-k)*n^k/k!), ", ")) \\ G. C. Greubel, May 13 2018
(PARI) a(n) = n!*pollaguerre(n, n*(n-1), -n); \\ Michel Marcus, Feb 05 2021
(Magma) [Factorial(n)*(&+[Binomial(n^2, n-k)*n^k/Factorial(k): k in [0..n]]): n in [0..25]]; // G. C. Greubel, May 13 2018

Crossrefs

Cf. A277373, A295385, A295406, A295407, A295408, A295409.

Sequence in context: A268557 A281183 A012209 * A172286 A129348 A280211

Adjacent sequences: A295415 A295416 A295417 * A295419 A295420 A295421

Keyword

nonn

Author

Vaclav Kotesovec, Nov 22 2017

Status

approved