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A370603
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a(n) = n! * Sum_{d|n} 1/((d-1)! * (n/d)!^(d-1)).
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3
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1, 4, 9, 40, 125, 936, 5047, 42848, 367929, 3668500, 39916811, 480577032, 6227020813, 87197480384, 1307761815375, 20923593490816, 355687428096017, 6402405005606628, 121645100408832019, 2432903231908929800, 51090944698284691221, 1124000756238680570272
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OFFSET
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1,2
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LINKS
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FORMULA
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If p is prime, a(p) = p + p!.
E.g.f.: Sum_{k>0} x^k * exp(x^k/k!).
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PROG
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(PARI) a(n) = n!*sumdiv(n, d, 1/((d-1)!*(n/d)!^(d-1)));
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, x^k*exp(x^k/k!))))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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