A306022 Stirling transform of partitions numbers (A000041).

1, 1, 3, 10, 38, 163, 774, 4006, 22376, 133951, 854402, 5775948, 41190317, 308651432, 2422315371, 19856073597, 169596622997, 1506139073454, 13879704561038, 132488897335228, 1307829322689944, 13330635710335512, 140118664473276174, 1516899115597189064

Offset: 0

Author

Vaclav Kotesovec, Jun 17 2018

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..571
• Eric Weisstein's World of Mathematics, Stirling Transform.

Crossrefs

Cf. A000041, A167137, A306023.

Programs

Maple

a:= n-> add(combinat[numbpart](j)*Stirling2(n, j), j=0..n):
seq(a(n), n=0..30);  # Alois P. Heinz, Jun 17 2018

Mathematica

Table[Sum[StirlingS2[n, k]*PartitionsP[k], {k, 0, n}], {n, 0, 25}]

PARI

a(n) = sum(k=0, n, stirling(n, k, 2)*numbpart(k)); \\ Michel Marcus, Jun 17 2018

Formula

a(n) = Sum_{k=0..n} Stirling2(n,k)*A000041(k).