A283337 Expansion of exp( Sum_{n>=1} -sigma_7(n)*x^n/n ) in powers of x.

1, -1, -64, -665, -1351, 33111, 408149, 1959491, -4502590, -149420286, -1182474566, -3678670450, 22384197409, 377982157035, 2474860645111, 6161653683590, -48899064011245, -695916857379611, -4275491639488601, -10750056317745704, 69316545348329853

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=6 of A283272.

Cf. A023875 (exp( Sum_{n>=1} sigma_7(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), this sequence (k=7), A283338 (k=8), A283339 (k=9), A283340 (k=10).

Formula

G.f.: Product_{n>=1} (1 - x^n)^(n^6).

a(n) = -(1/n)*Sum_{k=1..n} sigma_7(k)*a(n-k).