A294459 E.g.f.: exp(-Sum_{n>=1} A001227(n) * x^n).

1, -1, -1, -7, 25, -41, 631, 881, 98897, -609265, 3798991, -41799671, 914146729, -15008576857, 16469525255, -5181463756351, 79515495724321, -1220435382764129, 12608713897126687, -449855614172366695, 10437031873016276921, -231918657853281955081

Offset

0,4

Links

Seiichi Manyama, Table of n, a(n) for n = 0..446

Formula

a(0) = 1 and a(n) = (-1) * (n-1)! * Sum_{k=1..n} k*A001227(k)*a(n-k)/(n-k)! for n > 0.

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

Prog

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

Crossrefs

E.g.f.: exp(-Sum_{n>=1} (Sum_{d|n and d is odd} d^k) * x^n): this sequence (k=0), A294460 (k=1), A294461 (k=2).

Cf. A018804.

Sequence in context: A140716 A141393 A226366 * A075927 A119617 A102027

Adjacent sequences: A294456 A294457 A294458 * A294460 A294461 A294462

Keyword

sign

Author

Seiichi Manyama, Oct 31 2017

Status

approved