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A306022 Stirling transform of partitions numbers (A000041). 3
1, 1, 3, 10, 38, 163, 774, 4006, 22376, 133951, 854402, 5775948, 41190317, 308651432, 2422315371, 19856073597, 169596622997, 1506139073454, 13879704561038, 132488897335228, 1307829322689944, 13330635710335512, 140118664473276174, 1516899115597189064 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..23.

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: A103138 A074527 A338781 * A186367 A010842 A140710

Adjacent sequences:  A306019 A306020 A306021 * A306023 A306024 A306025

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Jun 17 2018

STATUS

approved

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Last modified April 20 18:08 EDT 2021. Contains 343135 sequences. (Running on oeis4.)