login
A306023
Stirling transform of partitions into distinct parts (A000009).
4
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
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
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Jun 17 2018
STATUS
approved