A295406 a(n) = n! * Laguerre(n, 2*n, -n).

1, 4, 58, 1422, 49000, 2174360, 118023264, 7574532826, 561071549056, 47111034709260, 4421715905632000, 458741213603157254, 52129735913348001792, 6439324687323193520608, 859089518697047400878080, 123108032319553206480143250, 18858657171509448248927617024

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..300

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(3*n,n-k)*n^k/k!.

a(n) ~ sqrt(1/2 + 5/(2*sqrt(13))) * ((11 + sqrt(13))/2)^n * exp((sqrt(13)-5)*n/2) * n^n.

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

Mathematica

Table[n!*LaguerreL[n, 2*n, -n], {n, 0, 15}]
Join[{1}, Table[n!*Sum[Binomial[3*n, n-k]*n^k/k!, {k, 0, n}], {n, 1, 15}]]

Prog

(PARI) for(n=0, 30, print1(n!*sum(k=0, n, binomial(3*n, n-k)*n^k/k!), ", ")) \\ G. C. Greubel, Feb 06 2018
(PARI) a(n) = n!*pollaguerre(n, 2*n, -n); \\ Michel Marcus, Feb 05 2021
(Magma) [Factorial(n)*(&+[Binomial(3*n, n-k)*n^k/Factorial(k): k in [0..n]]): n in [0..30]]; // G. C. Greubel, Feb 06 2018

Crossrefs

Cf. A277373, A295385, A295407, A295408.

Sequence in context: A334991 A216795 A216352 * A229528 A109056 A326944

Adjacent sequences: A295403 A295404 A295405 * A295407 A295408 A295409

Keyword

nonn

Author

Vaclav Kotesovec, Nov 22 2017

Status

approved