A306023 Stirling transform of partitions into distinct parts (A000009).

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

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..573

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: A150268 A369439 A165545 * A150269 A199822 A150270

Adjacent sequences: A306020 A306021 A306022 * A306024 A306025 A306026

Keyword

nonn

Author

Vaclav Kotesovec, Jun 17 2018

Status

approved