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%I #7 Apr 07 2012 17:12:47
%S 1,5,198,20548,4088918,1341552690,661685880676,460785157967228,
%T 432879460822014552,529918744425680488240,822575286838815581568992,
%U 1583737023708711008926884072,3713773722396456674797120593784,10445266376618187161982580673417192
%N E.g.f.: exp(-1)*Sum_{n>=0} (1+x)^(n^3)/n!.
%F a(n) = Sum_{k=0..n} Stirling1(n, k)*Bell(3*k).
%F a(n) = n!*exp(-1)*Sum_{k>=[n^(1/3)]} binomial(k^3,n)/k!.
%e E.g.f.: A(x) = 1 + 5*x + 198*x^2/2! + 20548*x^3/3! + 4088918*x^4/4! +...
%e such that
%e A(x) = exp(-1)*(1 + (1+x) + (1+x)^8/2! + (1+x)^27/3! + (1+x)^64/4! +...).
%o (PARI) {Stirling1(n, k)=n!*polcoeff(binomial(x, n), k)}
%o {Bell(n)=n!*polcoeff(exp(exp(x+x*O(x^n))-1), n)}
%o {a(n)=sum(k=0, n, Stirling1(n, k)*Bell(3*k))}
%o for(n=0,15,print1(a(n),", "))
%Y Cf. A000110 (Bell), A014507, A211251, A211252.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Apr 07 2012
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