OFFSET
1,2
FORMULA
a(n) = [x^n] (1/(1 - x)) * Sum_{k=1..n} (-1)^(n-k) * Stirling1(n,k) * x^k/(1 - x^k).
a(n) = Sum_{k=1..n} Sum_{d|k} (-1)^(n-d) * Stirling1(n,d).
MATHEMATICA
Table[Sum[(-1)^(n - k) StirlingS1[n, k] Floor[n/k] , {k, 1, n}], {n, 1, 22}]
Table[SeriesCoefficient[1/(1 - x) Sum[(-1)^(n - k) StirlingS1[n, k] x^k/(1 - x^k), {k, 1, n}], {x, 0, n}], {n, 1, 22}]
Table[Sum[Sum[(-1)^(n - d) StirlingS1[n, d], {d, Divisors[k]}], {k, 1, n}], {n, 1, 22}]
PROG
(PARI) a(n) = sum(k=1, n, (-1)^(n-k)*stirling(n, k, 1) * (n\k)); \\ Michel Marcus, Aug 23 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Aug 22 2019
STATUS
approved