

A356009


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


7



1, 4, 15, 73, 390, 2641, 19208, 164585, 1541746, 16158341, 181370552, 2283224065, 30160914446, 434715492485, 6655132252876, 109315669969217, 1879289179364690, 34719396682318021, 666070910669770400, 13590051478686198401, 289043813095242038422
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


LINKS

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


FORMULA

E.g.f.: (1/(1x)) * Sum_{k>0} (exp(x^k)  1)/k.
E.g.f.: (1/(1x)) * Sum_{k>0} log(1x^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)/(1x)))
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, log(1x^k)/k!)/(1x)))


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



