OFFSET
1,2
LINKS
Seiichi Manyama, Table of n, a(n) for n = 1..448
FORMULA
E.g.f.: (1/(1-x)) * Sum_{k>0} x^k/(k! * (1 - x^k)).
E.g.f.: (1/(1-x)) * Sum_{k>0} (exp(x^k) - 1).
a(n) = n! * Sum_{k=1..n} Sum_{d|k} 1/d! = n! * Sum_{k=1..n} A057625(k)/k!. - Seiichi Manyama, Aug 08 2022
PROG
(PARI) a(n) = n!*sum(k=1, n, n\k/k!);
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, x^k/(k!*(1-x^k)))/(1-x)))
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, exp(x^k)-1)/(1-x)))
(PARI) a(n) = n!*sum(k=1, n, sumdiv(k, d, 1/d!)); \\ Seiichi Manyama, Aug 08 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jul 20 2022
STATUS
approved