A356009 a(n) = n! * Sum_{k=1..n} Sum_{d|k} 1/(d * (k/d)!).

1, 4, 15, 73, 390, 2641, 19208, 164585, 1541746, 16158341, 181370552, 2283224065, 30160914446, 434715492485, 6655132252876, 109315669969217, 1879289179364690, 34719396682318021, 666070910669770400, 13590051478686198401, 289043813095242038422

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.

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*(k/d)!)));
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, (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. A087906, A356004.

Sequence in context: A171005 A303229 A340355 * A307996 A230741 A020082

Adjacent sequences: A356006 A356007 A356008 * A356010 A356011 A356012

Keyword

nonn

Author

Seiichi Manyama, Jul 23 2022

Status

approved