A294404 E.g.f.: exp(-Sum_{n>=1} sigma_2(n) * x^n).

1, -1, -9, -31, -23, 3399, 41311, 473129, 1284081, -79051537, -2447228249, -52444297071, -712806368999, -2221410364681, 331443685309647, 15068893004257049, 460836352976093281, 10298306504802529119, 122928784866003823831, -3359583359629857247807

Offset: 0

Author

Seiichi Manyama, Oct 30 2017

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..426

Crossrefs

E.g.f.: exp(-Sum_{n>=1} sigma_k(n) * x^n): A294402 (k=0), A294403 (k=1), this sequence (k=2).

Cf. A001157, A073592, A294362, A343497.

Programs

PARI

N=66; x='x+O('x^N); Vec(serlaplace(exp(-sum(k=1, N, sigma(k, 2)*x^k))))

Formula

a(0) = 1 and a(n) = (-1) * (n-1)! * Sum_{k=1..n} k*A001157(k)*a(n-k)/(n-k)! for n > 0.

E.g.f.: Product_{k>=1} (1 - x^k)^f(k), where f(k) = (1/k) * Sum_{j=1..k} gcd(k,j)^3. - Ilya Gutkovskiy, Aug 17 2021