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

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..571

Eric Weisstein's World of Mathematics, Stirling Transform.

Formula

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

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}]

Prog

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

Crossrefs

Cf. A000041, A167137, A306023.

Sequence in context: A359109 A346815 A351681 * A186367 A010842 A140710

Adjacent sequences: A306019 A306020 A306021 * A306023 A306024 A306025

Keyword

nonn

Author

Vaclav Kotesovec, Jun 17 2018

Status

approved