A283536 - OEIS

%I #14 Mar 13 2017 07:03:57

%S 1,-1,-64,-19619,-16755517,-30499543213,-101528172949440,

%T -558442022082754554,-4721800698082895269442,

%U -58144976385942395405449505,-999941534906642496357956893139,-23224150593200781968944997552887957,-708778584588517237886357058373629079824

%N Expansion of exp( Sum_{n>=1} -A283535(n)/n*x^n ) in powers of x.

%H Seiichi Manyama, <a href="/A283536/b283536.txt">Table of n, a(n) for n = 0..152</a>

%F G.f.: Product_{k>=1} (1 - x^k)^(k^(3*k)).

%F a(n) = -(1/n)*Sum_{k=1..n} A283535(k)*a(n-k) for n > 0.

%t A[n_] :=  Sum[d^(3*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, 12}] (* _Indranil Ghosh_, Mar 11 2017 *)

%o (PARI) A(n) = sumdiv(n, d, d^(3*d + 1));

%o a(n) = if(n==0, 1, -(1/n)*sum(k=1, n, A(k)*a(n - k)));

%o for(n=0, 12, print1(a(n), ", ")) \\ _Indranil Ghosh_, Mar 11 2017

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

%Y Cf. A283580 (Product_{k>=1} 1/(1 - x^k)^(k^(3*k))).

%K sign

%O 0,3

%A _Seiichi Manyama_, Mar 10 2017