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A327579 a(n) = n! * Sum_{d|n} d^(n/d) / d!. 2
1, 4, 9, 76, 125, 4686, 5047, 389768, 1995849, 62445610, 39916811, 23574862092, 6227020813, 5667436494734, 55630647072015, 2922249531801616, 355687428096017, 2425220588831040018, 121645100408832019, 1364553980880330240020, 18677216386213152768021, 1152100749379237026969622 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

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

FORMULA

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

MATHEMATICA

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

nmax = 22; CoefficientList[Series[Sum[x^k/((k - 1)! (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) / d!); \\ Michel Marcus, Sep 17 2019

CROSSREFS

Cf. A055225, A057625, A327578.

Sequence in context: A122956 A041777 A100517 * A041597 A041030 A061104

Adjacent sequences:  A327576 A327577 A327578 * A327580 A327581 A327582

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Sep 17 2019

STATUS

approved

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Last modified September 26 15:53 EDT 2021. Contains 347668 sequences. (Running on oeis4.)