A283339 Expansion of exp( Sum_{n>=1} -sigma_9(n)*x^n/n ) in powers of x.

1, -1, -256, -6305, -26335, 1321887, 32565169, 276211695, -2659962750, -111341327890, -1454216029918, -3323783801026, 227018039015019, 4636828146319845, 39615489757794355, -132865771935151820, -9075288352543844755, -132703303201618610765

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=8 of A283272.

Cf. A023877 (exp( Sum_{n>=1} sigma_9(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), A283338 (k=8), this sequence (k=9), A283340 (k=10).

Formula

G.f.: Product_{n>=1} (1 - x^n)^(n^8).

a(n) = -(1/n)*Sum_{k=1..n} sigma_9(k)*a(n-k).