A356401 a(n) = n! * Sum_{k=1..n} Sum_{d|k} (-1)^(d+1)/(d * (k/d)!).

1, 2, 9, 25, 150, 841, 6608, 41945, 437986, 4364741, 51640952, 526219585, 7319856206, 102469338245, 1671439939276, 23909485105217, 427384036676690, 7518024186420421, 149244833247716000, 2756811766466473601, 61545779138627817622, 1354007126970517958885

Offset

1,2

Links

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

Formula

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

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

Prog

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

Crossrefs

Cf. A356009, A356402.

Sequence in context: A093122 A305351 A101051 * A218460 A085070 A083383

Adjacent sequences: A356398 A356399 A356400 * A356402 A356403 A356404

Keyword

nonn

Author

Seiichi Manyama, Aug 05 2022

Status

approved