A344106 a(n) = n! * LaguerreL(n, -n+1).

1, 1, 7, 86, 1473, 32344, 866695, 27422352, 1000578817, 41361536384, 1910451937671, 97512721964800, 5450486787062977, 331112639931669504, 21722219855305516807, 1530517712811373819904, 115269154497700063898625, 9241045907270523509112832, 785719407951447904088069383

Offset

0,3

Links

Table of n, a(n) for n=0..18.

Formula

a(n) ~ exp((n-1)/phi - n) * phi^(2*n+1) * n^n / 5^(1/4), where phi = A001622 = (1+sqrt(5))/2 is the golden ratio.

a(n) = Sum_{k=0..n} binomial(n, k)^2*(n - k)!*(n - 1)^k. - Peter Luschny, Dec 25 2021

Mathematica

Table[n!*LaguerreL[n, -n+1], {n, 0, 20}]

Prog

(PARI) a(n) = n!*subst(pollaguerre(n), x, 1-n); \\ Michel Marcus, May 09 2021

Crossrefs

Cf. A001622, A277373, A343849, A344107.

Sequence in context: A296382 A296639 A220306 * A346987 A092586 A048363

Adjacent sequences: A344103 A344104 A344105 * A344107 A344108 A344109

Keyword

nonn

Author

Vaclav Kotesovec, May 09 2021

Status

approved