A288270 E.g.f.: exp(Sum_{k>=1} (k-1)^2*x^k).

1, 0, 2, 24, 228, 2400, 30360, 453600, 7702800, 144910080, 2981089440, 66561264000, 1603358729280, 41434803970560, 1142808612865920, 33485770103385600, 1038238875100627200, 33945895488708403200, 1166858228814204326400, 42055660151648798054400

Offset: 0

Author

Seiichi Manyama, Oct 20 2017

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..421

Crossrefs

E.g.f.: exp(Sum_{k>=1} (k-1)^m*x^k): A000262 (m=0), A052887 (m=1), this sequence (m=2), A290690 (m=3).

Cf. A255807.

Programs

PARI

{a(n) = n!*polcoeff(exp(sum(k=1, n, (k-1)^2*x^k)+x*O(x^n)), n)}

Formula

a(0) = 1 and a(n) = (n-1)! * Sum_{k=1..n} (k-1)^2*k*a(n-k)/(n-k)! for n > 0.

E.g.f.: exp(x^2*(1 + x)/(1 - x)^3). - Ilya Gutkovskiy, Jul 27 2020

a(n) ~ 2^(-7/8) * 3^(1/8) * n^(n - 1/8) / exp(n - 2^(9/4)*n^(3/4)/3^(3/4) + sqrt(2*n/3) - 2^(3/4)*n^(1/4)/3^(5/4) + 13/54). - Vaclav Kotesovec, Jul 31 2021