A370580 a(n) = (n-1)! * Sum_{d|n} d/(d-1)!.
1, 3, 5, 22, 29, 546, 727, 18488, 100809, 1164250, 3628811, 208232652, 479001613, 18741602894, 236107872015, 4796881689616, 20922789888017, 1618457192352018, 6402373705728019, 471378116297088020, 6105908234409984021, 153272981387362636822
Offset: 1
Programs
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PARI
a(n) = (n-1)!*sumdiv(n, d, d/(d-1)!);
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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) = p + (p-1)!.
E.g.f.: Sum_{k>0} x^k/k * exp(x^k).