A356011 a(n) = n! * Sum_{k=1..n} 1/(k! * floor(n/k)).

1, 2, 6, 17, 80, 337, 2240, 14681, 117010, 1023941, 10900472, 108881665, 1375544846, 17732140805, 247041590476, 3605768497217, 59990390084690, 977383707751621, 18214603019184800, 337615168055209601, 6763842079452393622, 141262515443311046885

Offset

1,2

Links

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

Formula

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

Prog

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

Crossrefs

Row sums of A356013.

Cf. A345682, A345683, A355991, A356015.

Sequence in context: A253882 A327698 A183757 * A181490 A340210 A165325

Adjacent sequences: A356008 A356009 A356010 * A356012 A356013 A356014

Keyword

nonn

Author

Seiichi Manyama, Jul 23 2022

Status

approved