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%I #16 Dec 11 2012 12:35:06
%S 1,1,4,51,1480,79765,7010496,920281831,169526669824,41844075277545,
%T 13357347571244800,5362349333225289691,2646862288162043664384,
%U 1576780272924188221429501,1116120717235502072828661760,926421799655193830945493519375,891516461371835173578650979598336
%N E.g.f.: 1/(1-x) = Sum_{n>=0} a(n) * exp(-n^2*x) * x^n/n!.
%C Compare to the identity: 1/(1-x) = Sum_{n>=0} n^n * exp(-n*x) * x^n/n!.
%C Compare to the o.g.f. of A007820:
%C Sum_{n>=0} S2(2*n,n)*x^n = Sum_{n>=0} (n^2)^n * exp(-n^2*x) * x^n/n!.
%e E.g.f.: 1/(1-x) = 1 + 1*exp(-x)*x + 4*exp(-2^2*x)*x^2/2! + 51*exp(-3^2*x)*x^3/3! + 1480*exp(-4^2*x)*x^4/4! + 79765*exp(-5^2*x)*x^5/5! + 7010496*exp(-6^2*x)*x^6/6!+...
%o (PARI) {a(n)=n!*polcoeff(1/(1-x+x*O(x^n))-sum(k=0,n-1,a(k)*x^k/k!*exp(-k^2*x+x*O(x^n))), n)}
%o for(n=0,16,print1(a(n),", "))
%Y Cf. A007820, A210029.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Dec 11 2012
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