A356009 a(n) = n! * Sum_{k=1..n} Sum_{d|k} 1/(d * (k/d)!).
1, 4, 15, 73, 390, 2641, 19208, 164585, 1541746, 16158341, 181370552, 2283224065, 30160914446, 434715492485, 6655132252876, 109315669969217, 1879289179364690, 34719396682318021, 666070910669770400, 13590051478686198401, 289043813095242038422
Offset: 1
Keywords
Programs
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Mathematica
Table[n! * Sum[Sum[1/(d*(k/d)!), {d,Divisors[k]}], {k,1,n}], {n,1,25}] (* Vaclav Kotesovec, Aug 11 2025 *) -
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))) -
PARI
my(N=30, x='x+O('x^N)); Vec(serlaplace(-sum(k=1, N, log(1-x^k)/k!)/(1-x)))
Formula
E.g.f.: (1/(1-x)) * Sum_{k>0} (exp(x^k) - 1)/k.
E.g.f.: -(1/(1-x)) * Sum_{k>0} log(1-x^k)/k!.