A277421 a(n) = n!*LaguerreL(n, -7*n).

1, 8, 254, 13614, 1025048, 99368620, 11781698256, 1651548277946, 267197019684224, 49000715036948304, 10044513851042988800, 2275926588768085912582, 564838094735322988575744, 152378369304839730672573044, 44397985962782115253758973952

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, A277420, A277422.

Cf. A002720, A087912, A277382.

Programs

Magma

[Factorial(n)*(&+[Binomial(n,k)*7^k*n^k/Factorial(k): k in [0..n]]): n in [0..30]]; // G. C. Greubel, May 15 2018

Mathematica

Table[n!*LaguerreL[n, -7*n], {n, 0, 20}]
Flatten[{1, Table[n!*Sum[Binomial[n, k] * 7^k * n^k / k!, {k, 0, n}], {n, 1, 20}]}]

PARI

for(n=0, 30, print1(n!*sum(k=0, n, binomial(n,k)*7^k*n^k/k!), ", ")) \\ G. C. Greubel, May 15 2018

Formula

a(n) = n! * Sum_{k=0..n} binomial(n, k) * 7^k * n^k / k!.

a(n) ~ sqrt(1/2 + 9/(2*sqrt(77))) * ((9 + sqrt(77))/2)^n * exp((-9 + sqrt(77))*n/2) * n^n.