A242858 E.g.f. ((e^x-1)^2*e^x) / (2*(1-(e^x-1)^3)).

0, 0, 1, 6, 25, 150, 1561, 16926, 181945, 2286150, 34082521, 548528046, 9363855865, 174531124950, 3547114323481, 76969474578366, 1771884893993785, 43405229295464550, 1128511554418948441, 30949983774936839886

Offset: 0

Author

Vladimir Kruchinin, May 24 2014

Keywords

• nonn

Programs

Mathematica

CoefficientList[Series[((Exp[x]-1)^2*Exp[x]) / (2*(1-(Exp[x]-1)^3)), {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, May 24 2014 *)

Maxima

a(n):=sum(((3*k)!*stirling2(n+1,3*k))/k,k,1,(n+1)/3)/6;

Formula

a(n) = sum(k=1..(n+1)/3, ((3*k)!*stirling2(n+1,3*k))/k)/6.

a(n) ~ n! / (6*(log(2))^(n+1)). - Vaclav Kotesovec, May 24 2014