A356004 a(n) = n! * Sum_{k=1..n} Sum_{d|k} 1/(d! * (k/d)!).
1, 4, 14, 64, 322, 2054, 14380, 116722, 1060580, 10636042, 116996464, 1411275650, 18346583452, 256869465610, 3856674412952, 61743633813634, 1049641774831780, 18896533652098442, 359034139389870400, 7182372973523436802, 150833211474559084844
Offset: 1
Keywords
Programs
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Mathematica
a[n_] := n! * Sum[DivisorSum[k, 1/(#!*(k/#)!) &], {k, 1, n}]; Array[a, 21] (* Amiram Eldar, Jul 22 2022 *) -
PARI
a(n) = n!*sum(k=1, n, sumdiv(k,d,1/(d!*(k/d)!)));
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PARI
my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, (exp(x^k)-1)/k!)/(1-x)))
Formula
E.g.f.: (1/(1-x)) * Sum_{k>0} (exp(x^k) - 1)/k!.
a(n) = n! * Sum_{k=1..n} A121860(k)/k!.