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E.g.f. ((e^x-1)^2*e^x) / (2*(1-(e^x-1)^3)).
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%I #7 May 26 2014 01:30:49

%S 0,0,1,6,25,150,1561,16926,181945,2286150,34082521,548528046,

%T 9363855865,174531124950,3547114323481,76969474578366,

%U 1771884893993785,43405229295464550,1128511554418948441,30949983774936839886

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

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

%F a(n) ~ n! / (6*(log(2))^(n+1)). - _Vaclav Kotesovec_, May 24 2014

%t 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 *)

%o (Maxima)

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

%K nonn

%O 0,4

%A _Vladimir Kruchinin_, May 24 2014