A355669 a(n) = n! * Sum_{d|n} (d!)^(d - n/d).

1, 6, 222, 331824, 24883200120, 139314069504005400, 82606411253903523840005040, 6984964247141514123629140377623274720, 109110688415571316480344899355894085582848000725760, 395940866122425193243875570782668457763038822400000006270570482400

Offset

1,2

Links

Table of n, a(n) for n=1..10.

Formula

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

Mathematica

a[n_] := n! * DivisorSum[n, (#!)^(# - n/#) &]; Array[a, 10] (* 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. A061095, A345465, A351165, A356662.

Sequence in context: A144658 A203637 A144045 * A061610 A054324 A117255

Adjacent sequences: A355666 A355667 A355668 * A355670 A355671 A355672

Keyword

nonn

Author

Seiichi Manyama, Aug 21 2022

Status

approved