A265024 a(n) = n! * Sum_{d in D(n+1)} (-1)^(d+1)*(n+1)/d, D(n) the divisors of n.

1, 1, 8, 6, 144, 480, 5760, 5040, 524160, 2177280, 43545600, 159667200, 6706022400, 49816166400, 2092278988800, 1307674368000, 376610217984000, 4623936565248000, 128047474114560000, 729870602452992000, 77852864261652480000, 613091306060513280000

Offset: 0

Author

Peter Luschny, Jan 26 2016

Keywords

• nonn

Crossrefs

Cf. A000593, A027750, A038048, A075525 (Bell transform).

Programs

Mathematica

Rest[CoefficientList[Series[Log[QPochhammer[-1, x]/2], {x, 0, 20}], x] * Range[0, 20]!] (* Vaclav Kotesovec, Oct 15 2017 *)

PARI

a(n) = n!*sumdiv(n+1, d, (-1)^(d+1)*(n+1)/d); \\ Michel Marcus, Jan 26 2016

Sage

A265024 = lambda n: factorial(n)*sum((-1)^(d+1)*(n+1)/d for d in divisors(n+1))
[A265024(n) for n in (0..21)]

Formula

E.g.f.: d/dx log(Product_{k>=1} (1 + x^k)). - Ilya Gutkovskiy, Oct 15 2017

a(n) = n! * A000593(n+1). - Seiichi Manyama, Nov 08 2020.

E.g.f.: d/dx ( Sum_{k>=1} x^k / (k * (1 - x^(2*k))) ). - Seiichi Manyama, Sep 18 2021