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A355886
a(n) = n! * Sum_{k=1..n} floor(n/k)/k!.
7
1, 5, 22, 125, 746, 5677, 44780, 420401, 4206970, 47543141, 562891352, 7573655905, 104684547566, 1596368400005, 25482043382476, 439969180782017, 7835163501390290, 151712475696833221, 3004182138648663200, 63854641556089628801, 1400563708969910620822
OFFSET
1,2
LINKS
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