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A265024
a(n) = n! * Sum_{d in D(n+1)} (-1)^(d+1)*(n+1)/d, D(n) the divisors of n.
10
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
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
KEYWORD
nonn
AUTHOR
Peter Luschny, Jan 26 2016
STATUS
approved