A370581 a(n) = n! * Sum_{d|n} d/(d! * (n/d)!).
1, 3, 4, 17, 6, 307, 8, 5049, 30250, 105851, 12, 25945933, 14, 77837775, 14529715216, 147891744017, 18, 13435316294419, 20, 7606841430988821, 16895152834560022, 183030822374423, 24, 387276381308571955225, 5385836820601036800026, 485735643993600027
Offset: 1
Programs
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PARI
a(n) = n!*sumdiv(n, d, d/(d!*(n/d)!));
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PARI
my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, x^k/k!*exp(x^k))))
Formula
If p is prime, a(p) = 1 + p.
E.g.f.: Sum_{k>0} x^k/k! * exp(x^k).