A283803 - OEIS

%I #12 Mar 17 2017 11:10:49

%S 1,-1,-256,-531185,-4294403215,-95363000657073,-4738284730302658391,

%T -459981771468075494207385,-79227701254823507875355278590,

%U -22528320196093613328344381426130010,-9999977451048811940735941180766259658078

%N Expansion of exp( Sum_{n>=1} -A283369(n)/n*x^n ) in powers of x.

%H Seiichi Manyama, <a href="/A283803/b283803.txt">Table of n, a(n) for n = 0..120</a>

%F G.f.: Product_{k>=1} (1 - x^k)^(k^(4*k)).

%F a(n) = -(1/n)*Sum_{k=1..n} A283369(k)*a(n-k) for n > 0.

%t CoefficientList[Series[Product[(1 - x^k)^(k^(4k)), {k, 1, 10}], {x, 0, 10}], x] (* _Indranil Ghosh_, Mar 17 2017 *)

%o (PARI) A(n) = sumdiv(n, d, d^(4*d + 1));

%o a(n) = if(n<1, 1, -(1/n) * sum(k=1, n, A(k) * a(n - k)));

%o for(n=0, 10, print1(a(n),", ")) \\ _Indranil Ghosh_, Mar 17 2017

%Y Cf. Product_{k>=1} (1 - x^k)^(k^(m*k)): A010815 (m=0), A283499 (m=1), A283534 (m=2), A283536 (m=3), this sequence (m=4).

%Y Cf. A283510 (Product_{k>=1} 1/(1 - x^k)^(k^(4*k))).

%K sign

%O 0,3

%A _Seiichi Manyama_, Mar 17 2017