A277420 a(n) = n!*LaguerreL(n, -6*n).

1, 7, 194, 9078, 596760, 50508120, 5228520912, 639915545808, 90390815432064, 14472947716917120, 2590274418097708800, 512433683486806447872, 111036605823697437490176, 26153418409614396515976192, 6653213794092052464421939200, 1817951594633556391548903168000

Offset: 0

Author

Vaclav Kotesovec, Oct 14 2016

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..250
• Eric Weisstein's World of Mathematics, Laguerre Polynomial
• Wikipedia, Laguerre polynomials

Crossrefs

Cf. A277373, A277391, A277392, A277418, A277419, A277421, A277422.

Cf. A002720, A087912, A277382.

Programs

Magma

[Factorial(n)*(&+[Binomial(n,k)*6^k*n^k/Factorial(k): k in [0..n]]): n in [0..30]]; // G. C. Greubel, May 15 2018

Mathematica

Table[n!*LaguerreL[n, -6*n], {n, 0, 20}]
Flatten[{1, Table[n!*Sum[Binomial[n, k] * 6^k * n^k / k!, {k, 0, n}], {n, 1, 20}]}]

PARI

for(n=0, 30, print1(n!*sum(k=0, n, binomial(n,k)*6^k*n^k/k!), ", ")) \\ G. C. Greubel, May 15 2018

Formula

a(n) = n! * Sum_{k=0..n} binomial(n, k) * 6^k * n^k / k!.

a(n) ~ sqrt(1/2 + 2/sqrt(15)) * (4 + sqrt(15))^n * exp((-4 + sqrt(15))*n) * n^n.