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

1, -1, -16, -713, -64687, -9688545, -2165715003, -675843665621, -280752874575386, -149800127959983890, -99844730502381895830, -81300082280849836639246, -79413710313923588156379547, -91652445699847071535357000689, -123383623610527054787988720527285, -191626051373071219208574650313032502

Offset: 0

Author

Seiichi Manyama, Mar 10 2017

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..214

Crossrefs

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

Cf. A283579 (Product_{k>=1} 1/(1 - x^k)^(k^(2*k))).

Programs

Mathematica

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 *)

PARI

a(n) = if(n==0, 1, -(1/n)*sum(k=1, n, sumdiv(k, d, d^(2*d + 1))*a(n - k)));
for(n=0, 15, print1(a(n), ", ")) \\ Indranil Ghosh, Mar 11 2017

Formula

G.f.: Product_{k>=1} (1 - x^k)^(k^(2*k)).

a(n) = -(1/n)*Sum_{k=1..n} A283533(k)*a(n-k) for n > 0.