A294460 E.g.f.: exp(-Sum_{n>=1} A000593(n) * x^n).

1, -1, -1, -19, 73, -401, 5191, -29779, 879089, -7232833, 103048111, -1891058291, 31696845049, -649348332049, 9310670445623, -270217657103731, 5480877008565601, -131578355696804609, 3133521575795986399, -81890613282163881043, 2460096066325021029161

Offset: 0

Author

Seiichi Manyama, Oct 31 2017

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..437

Crossrefs

E.g.f.: exp(-Sum_{n>=1} (Sum_{d|n and d is odd} d^k) * x^n): A294459 (k=0), this sequence (k=1), A294461 (k=2).

Cf. A000593, A081362, A294394.

Programs

PARI

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

Formula

a(0) = 1 and a(n) = (-1) * (n-1)! * Sum_{k=1..n} k*A000593(k)*a(n-k)/(n-k)! for n > 0.