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%I #2 Mar 30 2012 18:37:16
%S 1,2,26,732,116390,40513052,137522735588,643647384796344,
%T 34588935490621449862,3492521559898834682830380,
%U 2281778066215315012669841569932,2900138372618260977222563124493089544
%N G.f.: A(x) = exp( Sum_{n>=1} 2^(n^2)*sigma(n)*x^n/n ), a power series in x with integer coefficients.
%C Compare to g.f. of partition numbers: exp( Sum_{n>=1} sigma(n)*x^n/n ), where sigma(n) = A000203(n) is the sum of the divisors of n.
%e G.f.: A(x) = 1 + 2*x + 26*x^2 + 732*x^3 + 116390*x^4 + 40513052*x^5 +...
%e log(A(x)) = 2*x + 2^4*3*x^2/2 + 2^9*4*x^3/3 + 2^16*7*x^4/4 + 2^25*6*x^5/5 +...
%o (PARI) {a(n)=polcoeff(exp(sum(m=1,n,2^(m^2)*sigma(m)*x^m/m)+x*O(x^n)),n)}
%Y Cf. A000041, A000203.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Feb 06 2009
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