A356004 a(n) = n! * Sum_{k=1..n} Sum_{d|k} 1/(d! * (k/d)!).

1, 4, 14, 64, 322, 2054, 14380, 116722, 1060580, 10636042, 116996464, 1411275650, 18346583452, 256869465610, 3856674412952, 61743633813634, 1049641774831780, 18896533652098442, 359034139389870400, 7182372973523436802, 150833211474559084844

Offset

1,2

Links

Table of n, a(n) for n=1..21.

Formula

E.g.f.: (1/(1-x)) * Sum_{k>0} (exp(x^k) - 1)/k!.

a(n) = n! * Sum_{k=1..n} A121860(k)/k!.

Mathematica

a[n_] := n! * Sum[DivisorSum[k, 1/(#!*(k/#)!) &], {k, 1, n}]; Array[a, 21] (* Amiram Eldar, Jul 22 2022 *)

Prog

(PARI) a(n) = n!*sum(k=1, n, sumdiv(k, d, 1/(d!*(k/d)!)));
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, (exp(x^k)-1)/k!)/(1-x)))

Crossrefs

Cf. A002627, A121860, A355886, A355991.

Sequence in context: A357793 A341682 A242764 * A154407 A222467 A184265

Adjacent sequences: A356001 A356002 A356003 * A356005 A356006 A356007

Keyword

nonn

Author

Seiichi Manyama, Jul 22 2022

Status

approved