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

0,3

Links

Table of n, a(n) for n=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

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A248291 A038284 A264587 * A051762 A247017 A330142

Adjacent sequences: A265021 A265022 A265023 * A265025 A265026 A265027

Keyword

nonn

Author

Peter Luschny, Jan 26 2016

Status

approved