A283264 Expansion of exp( Sum_{n>=1} -sigma_4(n)*x^n/n ) in powers of x.

1, -1, -8, -19, -9, 127, 500, 1038, 448, -4967, -21463, -50043, -59084, 70418, 600080, 1837349, 3532062, 3179251, -6965009, -42260393, -119597290, -224546234, -223670132, 292245783, 2156083245, 6428174973, 13030612271, 16820582355, -133402359, -78307103593

Offset: 0

Author

Seiichi Manyama, Mar 04 2017

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..1000

Crossrefs

Column k=3 of A283272.

Cf. A023872 (exp( Sum_{n>=1} sigma_4(n)*x^n/n )).

Cf. exp( Sum_{n>=1} -sigma_k(n)*x^n/n ): A010815 (k=1), A073592 (k=2), A283263 (k=3), this sequence (k=4), A283271 (k=5).

Programs

SageMath

# uses[EulerTransform from A166861]
b = EulerTransform(lambda n: -n^3)
print([b(n) for n in range(30)]) # Peter Luschny, Nov 11 2020

Formula

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

a(n) = -(1/n)*Sum_{k=1..n} sigma_4(k)*a(n-k).