A332695 a(n) = (-1)^n * n! * Laguerre(n, 6*n).

1, 5, 98, 3234, 149784, 8927880, 650696400, 56061791856, 5574017768832, 628158472212096, 79123082415148800, 11015976349601752320, 1679832851707998600192, 278440504042352431942656, 49846084962712218734045184, 9584526091509128369970432000, 1970059291620925696814892810240

Offset: 0

Author

Vaclav Kotesovec, Feb 20 2020

Keywords

• nonn

Comments

For m > 4, (-1)^n * n! * Laguerre(n, m*n) ~ sqrt(1/2 + (m-2)/(2*sqrt(m*(m-4)))) * exp((m - 2 - sqrt(m*(m-4)))*n/2) * ((m - 2 + sqrt(m*(m-4)))/2)^n * n^n.

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..310

Crossrefs

Cf. A277420, A277423, A332692, A332693, A332679, A332694.

Programs

Mathematica

Table[(-1)^n * n! * LaguerreL[n, 6*n], {n, 0, 20}]
Flatten[{1, Table[n!*Sum[Binomial[n, k] * (-1)^(n-k) * 6^k * n^k / k!, {k, 0, n}], {n, 1, 20}]}]
Table[(-1)^n * n! * Hypergeometric1F1[-n, 1, 6*n], {n, 0, 20}]

PARI

a(n) = (-1)^n*n!*pollaguerre(n, 0, 6*n); \\ Michel Marcus, Feb 05 2021

Formula

a(n) ~ sqrt(1/2 + 1/sqrt(3)) * 2^n * exp((2-sqrt(3))*n) * ((1 + sqrt(3))/2)^(2*n) * n^n.