A309910 a(n) = Sum_{k=1..n} (-1)^(n-k) * Stirling1(n,k) * floor(n/k).

1, 3, 10, 53, 266, 2093, 14512, 134705, 1317724, 14339429, 156052942, 2243410945, 28893239818, 421448538895, 6810085942104, 117497037128065, 1980909279322608, 38790292385240321, 730946685781179418, 15916872348230275385, 346942995035062132634, 7767365425379382284307

Offset

1,2

Links

Table of n, a(n) for n=1..22.

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

Cf. A008275, A096308, A308812, A309911.

Sequence in context: A362062 A290489 A002873 * A042171 A133148 A189815

Adjacent sequences: A309907 A309908 A309909 * A309911 A309912 A309913

Keyword

nonn

Author

Ilya Gutkovskiy, Aug 22 2019

Status

approved