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A336997

a(n) = n! * Sum_{d|n} 2^(d - 1) / d!.

1, 4, 10, 56, 136, 1952, 5104, 94208, 605056, 7741952, 39917824, 1458295808, 6227024896, 175463616512, 2353813878784, 48886264659968, 355687428161536, 17362063156969472, 121645100409094144, 6001501553433509888, 85800344155030552576, 2248030289949388439552

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OFFSET

1,2

LINKS

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

FORMULA

E.g.f.: Sum_{k>=1} (exp(2*x^k) - 1) / 2.

a(p) = p! + 2^(p - 1), where p is prime.

MATHEMATICA

Table[n! Sum[2^(d - 1)/d!, {d, Divisors[n]}], {n, 1, 22}]

nmax = 22; CoefficientList[Series[Sum[(Exp[2 x^k] - 1)/2, {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]! // Rest

PROG