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A330020 Expansion of e.g.f. Sum_{k>=1} x^k / (k! * (1 - x^k)^k). 0
1, 3, 7, 49, 121, 2161, 5041, 127681, 725761, 12852001, 39916801, 2917918081, 6227020801, 392423391361, 4740319584001, 122053759027201, 355687428096001, 57808258040332801, 121645100408832001, 18854997267794688001, 289799177540640768001, 7306005040298918553601 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..22.

FORMULA

a(n) = n! * Sum_{d|n} (d + n/d - 2)! / (d! * (d - 1)! * (n/d - 1)!).

MATHEMATICA

nmax = 22; CoefficientList[Series[Sum[x^k/(k! (1 - x^k)^k), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]! // Rest

a[n_] := n! Sum[(d + n/d - 2)!/(d! (d - 1)! (n/d - 1)!), {d, Divisors[n]}]; Table[a[n], {n, 1, 22}]

CROSSREFS

Cf. A057625, A157019, A327578, A327579.

Sequence in context: A173771 A019039 A077559 * A327578 A062959 A275830

Adjacent sequences:  A330017 A330018 A330019 * A330021 A330022 A330023

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Nov 27 2019

STATUS

approved

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Last modified October 24 05:38 EDT 2021. Contains 348217 sequences. (Running on oeis4.)