A283340 Expansion of exp( Sum_{n>=1} -sigma_10(n)*x^n/n ) in powers of x.

1, -1, -512, -19171, -111645, 8255899, 287477144, 3248973702, -56353404842, -2946880278857, -50078654012311, -24091665240825, 19437354184565824, 486126425619195338, 4607922953609319032, -63107867988829247005, -3101395214088243725145

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=9 of A283272.

Cf. A023878 (exp( Sum_{n>=1} sigma_10(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), A283339 (k=9), this sequence (k=10).

Formula

G.f.: Product_{n>=1} (1 - x^n)^(n^9).

a(n) = -(1/n)*Sum_{k=1..n} sigma_10(k)*a(n-k).