A327578 a(n) = n! * Sum_{d|n} d^(n/d - 1) / d!.

1, 3, 7, 49, 121, 2521, 5041, 208321, 907201, 32810401, 39916801, 10621860481, 6227020801, 2877004690561, 19233710496001, 1415779600435201, 355687428096001, 1085522620595212801, 121645100408832001, 653741050484890368001, 6259137133527742464001, 576612373659657208473601

Offset

1,2

Links

Seiichi Manyama, Table of n, a(n) for n = 1..425

Formula

E.g.f.: Sum_{k>=1} x^k / (k! * (1 - k * x^k)).

Mathematica

a[n_] := n! Sum[d^(n/d - 1)/d!, {d, Divisors[n]}]; Table[a[n], {n, 1, 22}]
nmax = 22; CoefficientList[Series[Sum[x^k/(k! (1 - k x^k)), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]! // Rest

Prog

(PARI) a(n) = n! * sumdiv(n, d, d^(n/d - 1) / d!); \\ Michel Marcus, Sep 17 2019

Crossrefs

Cf. A057625, A087909, A327579.

Sequence in context: A077559 A330020 A354845 * A358593 A062959 A275830

Adjacent sequences: A327575 A327576 A327577 * A327579 A327580 A327581

Keyword

nonn

Author

Ilya Gutkovskiy, Sep 17 2019

Status

approved