A283338 Expansion of exp( Sum_{n>=1} -sigma_8(n)*x^n/n ) in powers of x.

1, -1, -128, -2059, -6069, 210067, 3664420, 23366098, -116899962, -4133365357, -41809923367, -125160180169, 2447495850838, 42931762306584, 321967686614676, 281683012498569, -23874414003295851, -318729240693402530, -1992572289343189863

Offset: 0

Author

Seiichi Manyama, Mar 05 2017

Keywords

• sign

Links

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

Crossrefs

Column k=7 of A283272.

Cf. A023876 (exp( Sum_{n>=1} sigma_8(n)*x^n/n )).

Cf. exp( Sum_{n>=1} -sigma_k(n)*x^n/n ): A010815 (k=1), A073592 (k=2), A283263 (k=3), A283264 (k=4), A283271 (k=5), A283336 (k=6), A283337 (k=7), this sequence (k=8), A283339 (k=9), A283340 (k=10).

Formula

G.f.: Product_{n>=1} (1 - x^n)^(n^7).

a(n) = -(1/n)*Sum_{k=1..n} sigma_8(k)*a(n-k).