A344107 a(n) = n! * LaguerreL(n, -n+2).

1, 0, 2, 34, 648, 14988, 414160, 13373190, 495057024, 20686611736, 963532779264, 49510386761130, 2782552712473600, 169808382346687524, 11182975029610555392, 790535958617173397902, 59708339321680507207680, 4798728602043471360126000, 408910082803875174679773184

Offset: 0

Author

Vaclav Kotesovec, May 09 2021

Keywords

• nonn

Comments

In general, for fixed k>=0, n!*LaguerreL(n, -n+k) ~ exp((n-k)/phi - n) * phi^(2*n+1) * n^n / 5^(1/4).

Crossrefs

Cf. A001622, A277373, A343849, A344106.

Programs

Mathematica

Table[n!*LaguerreL[n, -n+2], {n, 0, 20}]

PARI

a(n) = n!*subst(pollaguerre(n), x, 2-n); \\ Michel Marcus, May 09 2021

Formula

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