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%I #4 Sep 30 2015 21:59:42
%S 1,2,14,204,16982,6746636,11467009772,80444425963128,
%T 2306004014991374374,268654794950955551450892,
%U 126765597355485863873077402788,241678070949320869650125781001909864
%N G.f.: A(x) = exp( Sum_{n>=1} x^n/n * 2^(n^2)/(1 - 2^(n^2)*x^n) ).
%C Compare to g.f. of the partition numbers A000041:
%C exp( Sum_{n>=1} x^n/(1 - x^n)/n ) = 1 + x + 2*x^2 + 3*x^3 + 5*x^4 +...
%F G.f.: exp( Sum_{n>=1} x^n/n * Sum_{d|n} 2^(n*d) * n/d ).
%e G.f.: A(x) = 1 + 2*x + 14*x^2 + 204*x^3 + 16982*x^4 + 6746636*x^5 +...
%e log(A(x)) = 2*x + 24*x^2/2 + 536*x^3/3 + 66112*x^4/4 + 33554592*x^5/5 +...
%e log(A(x)) = 2*x/(1-2*x) + 2^4*x^2/(1-2^4*x^2)/2 + 2^9*x^3/(1-2^9*x^3)/3 +...
%o (PARI) {a(n)=if(n==0,1,polcoeff(exp(sum(k=1,n,(2^k*x)^k/(1-(2^k*x)^k +x*O(x^n))/k)),n))}
%o for(n=0, 15, print1(a(n), ", "))
%o (PARI) {a(n) = polcoeff( exp( sum(m=1, n, x^m/m * sumdiv(m, d, 2^(m*d) * m/d) ) +x*O(x^n)), n)}
%o for(n=0, 15, print1(a(n), ", ")) \\ _Paul D. Hanna_, Sep 30 2015
%Y Cf. A158096, A155200.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Mar 26 2009
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