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A283534 Expansion of exp( Sum_{n>=1} -A283533(n)/n*x^n ) in powers of x.

%I A283534 #17 Mar 13 2017 07:03:31
%S A283534 1,-1,-16,-713,-64687,-9688545,-2165715003,-675843665621,
%T A283534 -280752874575386,-149800127959983890,-99844730502381895830,
%U A283534 -81300082280849836639246,-79413710313923588156379547,-91652445699847071535357000689,-123383623610527054787988720527285,-191626051373071219208574650313032502
%N A283534 Expansion of exp( Sum_{n>=1} -A283533(n)/n*x^n ) in powers of x.
%H A283534 Seiichi Manyama, <a href="/A283534/b283534.txt">Table of n, a(n) for n = 0..214</a>
%F A283534 G.f.: Product_{k>=1} (1 - x^k)^(k^(2*k)).
%F A283534 a(n) = -(1/n)*Sum_{k=1..n} A283533(k)*a(n-k) for n > 0.
%t A283534 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 A283534 (PARI)
%o A283534 a(n) = if(n==0, 1, -(1/n)*sum(k=1, n, sumdiv(k, d, d^(2*d + 1))*a(n - k)));
%o A283534 for(n=0, 15, print1(a(n), ", ")) \\ _Indranil Ghosh_, Mar 11 2017
%Y A283534 Cf. Product_{k>=1} (1 - x^k)^(k^(m*k)): A010815 (m=0), A283499 (m=1), this sequence (m=2), A283536 (m=3).
%Y A283534 Cf. A283579 (Product_{k>=1} 1/(1 - x^k)^(k^(2*k))).
%K A283534 sign
%O A283534 0,3
%A A283534 _Seiichi Manyama_, Mar 10 2017