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A283579 Expansion of exp( Sum_{n>=1} A283533(n)/n*x^n ) in powers of x.

%I A283579 #18 Mar 17 2017 07:44:28
%S A283579 1,1,17,746,66418,9843707,2187941520,680615139257,282199700198462,
%T A283579 150389915598653924,100155578743010743914,81505577512720707466924,
%U A283579 79580089689432499741178617,91814299713761739807846854872
%N A283579 Expansion of exp( Sum_{n>=1} A283533(n)/n*x^n ) in powers of x.
%H A283579 Seiichi Manyama, <a href="/A283579/b283579.txt">Table of n, a(n) for n = 0..214</a>
%F A283579 G.f.: Product_{k>=1} 1/(1 - x^k)^(k^(2*k)).
%F A283579 a(n) = (1/n)*Sum_{k=1..n} A283533(k)*a(n-k) for n > 0.
%F A283579 a(n) ~ n^(2*n) * (1 + exp(-2)/n^2). - _Vaclav Kotesovec_, Mar 17 2017
%t A283579 A[n_] :=  Sum[d^(2*d + 1), {d, Divisors[n]}]; a[n_] := If[n==0, 1, (1/n)*Sum[A[k]*a[n - k], {k, n}]]; Table[a[n], {n, 0, 13}] (* _Indranil Ghosh_, Mar 11 2017 *)
%o A283579 (PARI) A(n) = sumdiv(n, d, d^(2*d + 1));
%o A283579 a(n) = if(n==0, 1, (1/n)*sum(k=1, n, A(k)*a(n - k)));
%o A283579 for(n=0, 11, print1(a(n),", ")) \\ _Indranil Ghosh_, Mar 11 2017
%Y A283579 Cf. Product_{k>=1} 1/(1 - x^k)^(k^(m*k)): A000041 (m=0), A023880 (m=1), this sequence (m=2), A283580 (m=3).
%Y A283579 Cf. A283534 (Product_{k>=1} (1 - x^k)^(k^(2*k))).
%K A283579 nonn
%O A283579 0,3
%A A283579 _Seiichi Manyama_, Mar 11 2017