A309911 a(n) = Sum_{k=1..n} Stirling2(n,k) * floor(n/k).

1, 3, 7, 25, 71, 360, 1310, 7195, 35740, 213318, 1132154, 8409475, 50344672, 366939569, 2728237607, 21375289293, 159969524749, 1462761108082, 11896122581676, 107011124829787, 1031744001100166, 9684995830526129, 91735916202054984, 1010641832989185386, 10131466944871497886

Offset: 1

Author

Ilya Gutkovskiy, Aug 22 2019

Keywords

• nonn

Crossrefs

Cf. A008277, A308037, A308812, A309910.

Programs

Mathematica

Table[Sum[StirlingS2[n, k] Floor[n/k] , {k, 1, n}], {n, 1, 25}]
Table[SeriesCoefficient[1/(1 - x) Sum[StirlingS2[n, k] x^k/(1 - x^k), {k, 1, n}], {x, 0, n}], {n, 1, 25}]
Table[Sum[Sum[StirlingS2[n, d], {d, Divisors[k]}], {k, 1, n}], {n, 1, 25}]

PARI

a(n) = sum(k=1, n, stirling(n, k, 2) * (n\k)); \\ Michel Marcus, Aug 23 2019

Formula

a(n) = [x^n] (1/(1 - x)) * Sum_{k=1..n} Stirling2(n,k) * x^k/(1 - x^k).

a(n) = Sum_{k=1..n} Sum_{d|k} Stirling2(n,d).