A283335 Expansion of exp( Sum_{n>=1} -A062796(n)/n*x^n ) in powers of x.

1, -1, -2, -7, -54, -544, -7005, -108220, -1958263, -40629205, -951376217, -24826365255, -714568797261, -22491957589783, -768651303338761, -28344950796904518, -1121910285249842486, -47442295013058570884, -2134673855370621621400

Offset: 0

Author

Seiichi Manyama, Mar 08 2017

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..387

Crossrefs

Cf. A023879 (exp( Sum_{n>=1} A062796(n)/n*x^n )), A062796.

Programs

Mathematica

A[n_] :=  Sum[d^d, {d, Divisors[n]}]; a[n_] := If[n==0, 1, -(1/n)*Sum[A[k]*a[n - k], {k, n}]]; Table[a[n], {n, 0, 18}] (* Indranil Ghosh, Mar 11 2017 *)

PARI

a(n) = if(n==0, 1, -(1/n)*sum(k=1, n, sumdiv(k, d, d^d)*a(n - k)));
for(n=0, 18, print1(a(n), ", ")) \\ Indranil Ghosh, Mar 11 2017

Formula

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

a(n) = -(1/n)*Sum_{k=1..n} A062796(k)*a(n-k) for n > 0.