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%I #3 Nov 06 2012 20:03:09
%S 1,1,3,16,111,911,8622,91414,1067579,13564195,185687381,2718184470,
%T 42288343176,695667651368,12049465530936,218945489692574,
%U 4160440403683643,82448824370010887,1699889286488298603,36384381642357676480,806926050321577391347,18510872795071148287531
%N O.g.f.: A(x) = Sum_{n>=0} n^n*x^n/(1-n*x)^(2*n)/n! * exp(-n*x/(1-n*x)^2).
%e O.g.f.: A(x) = 1 + x + 3*x^2 + 16*x^3 + 111*x^4 + 911*x^5 + 8622*x^6 +...
%e where
%e A(x) = 1 + x/(1-x)^2*exp(-x/(1-x)^2) + 2^2*x^2/(1-2*x)^4/2!*exp(-2*x/(1-2*x)^2) + 3^3*x^3/(1-3*x)^6/3!*exp(-3*x/(1-3*x)^2) + 4^4*x^4/(1-4*x)^8/4!*exp(-4*x/(1-4*x)^2) + 5^5*x^5/(1-5*x)^10/5!*exp(-5*x/(1-5*x)^2) +...
%e simplifies to a power series in x with integer coefficients.
%o (PARI) {a(n)=local(A=1+x);A=sum(k=0,n,k^k/(1-k*x)^(2*k)*x^k/k!*exp(-k*x/(1-k*x)^2+x*O(x^n)));polcoeff(A,n)}
%o for(n=0,25,print1(a(n),", "))
%Y Cf. A134055.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Nov 06 2012
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