A332679 a(n) = (-1)^n * n! * Laguerre(n, 4*n).

1, 3, 34, 642, 16920, 571880, 23577552, 1147008912, 64304389504, 4081584090240, 289302692908800, 22648001532831488, 1940655970832219136, 180654087647513945088, 18153823412468554639360, 1958590905998560664832000, 225799980396482832660529152, 27702168947661388727726931968

Offset: 0

Author

Vaclav Kotesovec, Feb 19 2020

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..335

Crossrefs

Cf. A277423, A332692, A332693, A332694, A332695.

Cf. A277418, A295408, A302112, A332680.

Programs

Mathematica

Table[(-1)^n*n!*LaguerreL[n, 4*n], {n, 0, 20}]
Join[{1}, Table[n! * Sum[(-1)^(n-k) * Binomial[n, k] * (4*n)^k/k!, {k, 0, n}], {n, 1, 20}]]
Table[(-1)^n*n!*Hypergeometric1F1[-n, 1, 4*n], {n, 0, 20}]

PARI

a(n) = (-1)^n*n!*pollaguerre(n, 0, 4*n); \\ Michel Marcus, Feb 05 2021

Formula

A302112(n) = (a(n) - 2*n*A332680(n)) * binomial(2*n, n) / 2^n.

a(n) / (n*A332680(n)) ~ 2.

a(n) ~ c * n^(n + 1/6) * exp(n), where c = Gamma(1/3) / (2^(5/6) * 3^(1/6) * sqrt(Pi)) = 0.706332637459...