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A356662
a(n) = n! * Sum_{d|n} 1/(d!)^(n/d - 1).
2
1, 4, 12, 60, 240, 1740, 10080, 87360, 735840, 7514640, 79833600, 976686480, 12454041600, 175736040480, 2616448554720, 42011071502400, 711374856192000, 12830610027755520, 243290200817664000, 4870565189425615680, 102182981410948838400, 2249099140674523737600
OFFSET
1,2
FORMULA
a(p) = 2 * p! for prime p.
E.g.f.: Sum_{k>=1} x^k/(1 - x^k/k!).
MATHEMATICA
a[n_] := n! * DivisorSum[n, 1/(#!)^(n/# - 1) &]; Array[a, 22] (* Amiram Eldar, Aug 21 2022 *)
PROG
(PARI) a(n) = n!*sumdiv(n, d, 1/d!^(n/d-1));
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, x^k/(1-x^k/k!))))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Aug 21 2022
STATUS
approved