A308351 For n >= 2, a(n) = n*u(n-1) + n*(n-1)*u(n-2), where u = A292932; a(1)=1.

1, 4, 18, 128, 1090, 11232, 134806, 1849696, 28550538, 489656720, 9237631150, 190115847792, 4238752713442, 101775333547552, 2618244556598310, 71846664091504064, 2094748778352174202, 64666725024407102064, 2107224874854168508126, 72279858915240296971600

Offset: 1

Author

J. Devillet, May 21 2019

Keywords

• nonn
• easy

Links

• Robert Israel, Table of n, a(n) for n = 1..412
• M. Couceiro, J. Devillet, All quasitrivial n-ary semigroups are reducible to semigroups, arXiv:1904.05968 [math.RA], 2019.

Crossrefs

Cf. A292932, A292933.

Programs

Maple

E:= x*(1 + x)/(3 - 2*exp(x) + x):
S:= series(E,x,51):
seq(coeff(S,x,n)*n!,n=1..50); # Robert Israel, Nov 26 2020

Mathematica

nmax = 20; Rest[CoefficientList[Series[x*(1 + x)/(3 - 2*E^x + x), {x, 0, nmax}], x] * Range[0, nmax]!] (* Vaclav Kotesovec, Jun 05 2019 *)

Formula

a(n) = n*A292932(n-1) + n*(n-1)*A292932(n-2) = A292933(n) + n*A292933(n-1) for n >= 2.

E.g.f.: x*(1 + x)/(3 - 2*exp(x) + x). - Vaclav Kotesovec, Jun 05 2019

a(n) ~ n! * (r-2) / ((r-1) * (r-3)^n), where r = -LambertW(-1, -2*exp(-3)). - Vaclav Kotesovec, Jun 05 2019