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A327579
a(n) = n! * Sum_{d|n} d^(n/d) / d!.
5
1, 4, 9, 76, 125, 4686, 5047, 389768, 1995849, 62445610, 39916811, 23574862092, 6227020813, 5667436494734, 55630647072015, 2922249531801616, 355687428096017, 2425220588831040018, 121645100408832019, 1364553980880330240020, 18677216386213152768021, 1152100749379237026969622
OFFSET
1,2
LINKS
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
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Sep 17 2019
STATUS
approved