A087905 a(n) = n! * Sum_{d|n} (d/n)^d.

1, 3, 8, 36, 144, 1010, 5760, 50400, 416640, 4250232, 43545600, 553106400, 6706022400, 95865541200, 1410695430144, 22720842144000, 376610217984000, 6888030445296000, 128047474114560000, 2587520533615041024

Offset: 1

Author

Vladeta Jovovic, Oct 14 2003

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..445

Crossrefs

Cf. A061095, A038041, A057625, A038048, A005225.

Programs

Mathematica

a[n_]:= n!*DivisorSum[n, (#/n)^# &]; Array[a, 50] (* G. C. Greubel, May 16 2018 *)

PARI

{a(n)= n!*sumdiv(n, d, (d/n)^d)};
for(n=1, 30, print1(a(n), ", ")) \\ G. C. Greubel, May 16 2018

Formula

E.g.f.: Sum_{k>0} x^k/(k-x^k).