This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A306023 #12 Feb 16 2025 08:33:54
%S A306023 1,1,2,6,22,89,391,1875,9822,55817,340535,2208681,15118109,108677575,
%T A306023 817914056,6431115486,52741729600,450432487463,3999401133601,
%U A306023 36853795902353,351799243932131,3472526583025397,35382850151528847,371592232539942447,4016792440158613798
%N A306023 Stirling transform of partitions into distinct parts (A000009).
%H A306023 Alois P. Heinz, <a href="/A306023/b306023.txt">Table of n, a(n) for n = 0..573</a>
%H A306023 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/StirlingTransform.html">Stirling Transform</a>.
%F A306023 a(n) = Sum_{k=0..n} Stirling2(n,k)*A000009(k).
%p A306023 b:= proc(n) option remember; `if`(n=0, 1, add(b(n-j)*add(
%p A306023 `if`(d::odd, d, 0), d=numtheory[divisors](j)), j=1..n)/n)
%p A306023 end:
%p A306023 a:= n-> add(b(j)*Stirling2(n, j), j=0..n):
%p A306023 seq(a(n), n=0..30); # _Alois P. Heinz_, Jun 17 2018
%t A306023 Table[Sum[StirlingS2[n, k]*PartitionsQ[k], {k, 0, n}], {n, 0, 25}]
%Y A306023 Cf. A000009, A305550, A306022.
%K A306023 nonn
%O A306023 0,3
%A A306023 _Vaclav Kotesovec_, Jun 17 2018