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A370602
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a(n) = n! * Sum_{d|n} 1/((d-1)! * (n/d)^(d-1)).
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2
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1, 4, 9, 40, 125, 1056, 5047, 51248, 383049, 4364020, 39916811, 576885552, 6227020813, 99634224704, 1334500527375, 23592657488416, 355687428096017, 7202890599354468, 121645100408832019, 2679832071577681040, 51612375654647808021, 1226182612423511392672
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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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