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A306023 Stirling transform of partitions into distinct parts (A000009). 3
1, 1, 2, 6, 22, 89, 391, 1875, 9822, 55817, 340535, 2208681, 15118109, 108677575, 817914056, 6431115486, 52741729600, 450432487463, 3999401133601, 36853795902353, 351799243932131, 3472526583025397, 35382850151528847, 371592232539942447, 4016792440158613798 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..24.

Eric Weisstein's World of Mathematics, Stirling Transform.

FORMULA

a(n) = Sum_{k=0..n} Stirling2(n,k)*A000009(k).

MAPLE

b:= proc(n) option remember; `if`(n=0, 1, add(b(n-j)*add(

     `if`(d::odd, d, 0), d=numtheory[divisors](j)), j=1..n)/n)

    end:

a:= n-> add(b(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]*PartitionsQ[k], {k, 0, n}], {n, 0, 25}]

CROSSREFS

Cf. A000009, A305550, A306022.

Sequence in context: A165544 A150268 A165545 * A150269 A199822 A150270

Adjacent sequences:  A306020 A306021 A306022 * A306024 A306025 A306026

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Jun 17 2018

STATUS

approved

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Last modified April 15 04:04 EDT 2021. Contains 342974 sequences. (Running on oeis4.)