A283536 Expansion of exp( Sum_{n>=1} -A283535(n)/n*x^n ) in powers of x.

1, -1, -64, -19619, -16755517, -30499543213, -101528172949440, -558442022082754554, -4721800698082895269442, -58144976385942395405449505, -999941534906642496357956893139, -23224150593200781968944997552887957, -708778584588517237886357058373629079824

Offset: 0

Author

Seiichi Manyama, Mar 10 2017

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..152

Crossrefs

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

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

Programs

Mathematica

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 *)

PARI

A(n) = sumdiv(n, d, d^(3*d + 1));
a(n) = if(n==0, 1, -(1/n)*sum(k=1, n, A(k)*a(n - k)));
for(n=0, 12, print1(a(n), ", ")) \\ Indranil Ghosh, Mar 11 2017

Formula

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

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