A351165 a(n) = n! * Sum_{d|n} d^(d - n/d).

1, 6, 60, 1584, 75120, 5601960, 592956000, 84557864160, 15620794842240, 3628800457682400, 1035338990353113600, 355902198996315787200, 145077660657865961625600, 69194697633957032681544000, 38174841090323471644830720000, 24122334398251368151021076928000

Offset

1,2

Links

Table of n, a(n) for n=1..16.

Formula

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

Mathematica

a[n_] := n! * DivisorSum[n, #^(# - n/#) &]; Array[a, 16] (* Amiram Eldar, Aug 21 2022 *)

Prog

(PARI) a(n) = n!*sumdiv(n, d, d^(d-n/d));
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, (k*x)^k/(k-x^k))))

Crossrefs

Cf. A062796, A087905, A355669, A356661.

Sequence in context: A001416 A251184 A329319 * A003267 A271681 A010574

Adjacent sequences: A351162 A351163 A351164 * A351166 A351167 A351168

Keyword

nonn

Author

Seiichi Manyama, Aug 21 2022

Status

approved