A370579 - OEIS

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A370579

a(n) = n! * Sum_{d|n} 1/(d-1)!.

1, 4, 9, 52, 125, 1806, 5047, 87368, 544329, 7408810, 39916811, 1281329292, 6227020813, 174477663374, 2015997984015, 45336862771216, 355687428096017, 16059446167564818, 121645100408832019, 5372665305815808020, 76707372899469312021, 2248001765299683993622

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

Table of n, a(n) for n=1..22.

FORMULA

a(n) = n * A087906(n).

If p is prime, a(p) = p + p!.

E.g.f.: Sum_{k>0} x^k * exp(x^k).

PROG

(PARI) a(n) = n!*sumdiv(n, d, 1/(d-1)!);

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, x^k*exp(x^k))))