A356011 a(n) = n! * Sum_{k=1..n} 1/(k! * floor(n/k)).
1, 2, 6, 17, 80, 337, 2240, 14681, 117010, 1023941, 10900472, 108881665, 1375544846, 17732140805, 247041590476, 3605768497217, 59990390084690, 977383707751621, 18214603019184800, 337615168055209601, 6763842079452393622, 141262515443311046885
Offset: 1
Keywords
Programs
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Mathematica
Table[n! * Sum[1/(k!*Floor[n/k]), {k,1,n}], {n,1,25}] (* Vaclav Kotesovec, Aug 11 2025 *) -
PARI
a(n) = n!*sum(k=1, n, 1/(k!*(n\k)));
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PARI
my(N=30, x='x+O('x^N)); Vec(serlaplace(-sum(k=1, N, (1-x^k)*log(1-x^k)/k!)/(1-x)))
Formula
E.g.f.: -(1/(1-x)) * Sum_{k>0} (1 - x^k) * log(1 - x^k)/k!.
a(n) ~ exp(1) * (n-1)!. - Vaclav Kotesovec, Aug 11 2025