A283499 Expansion of exp( Sum_{n>=1} -A283498(n)/n*x^n ) in powers of x.

1, -1, -4, -23, -223, -2767, -42268, -759008, -15672223, -365639304, -9512549191, -273072804420, -8575012101043, -292422232720311, -10762617713743350, -425245537127322111, -17953822507629389009, -806668679245000383731

Offset: 0

Author

Seiichi Manyama, Mar 09 2017

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..386

Crossrefs

Cf. A023880, A283498.

Programs

Mathematica

A[n_] :=  Sum[d^(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, 17}] (* Indranil Ghosh, Mar 11 2017 *)

PARI

a(n) = if(n==0, 1, -(1/n)*sum(k=1, n, sumdiv(k, d, d^(d + 1))*a(n - k)));
for(n=0, 20, print1(a(n), ", ")) \\ Indranil Ghosh, Mar 11 2017

Formula

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

a(n) = -(1/n)*Sum_{k=1..n} A283498(k)*a(n-k) for n > 0.