cp's OEIS Frontend

A290352 Euler transform of the Fubini numbers (ordered Bell numbers, A000670).

%I A290352 #14 Aug 10 2021 18:27:20
%S A290352 1,1,4,17,98,678,5687,55656,626161,7963511,113027113,1770785023,
%T A290352 30346490633,564546034917,11327726548719,243811768229012,
%U A290352 5602495216123312,136878883607160468,3542830077444873188,96835203745704714722,2787051847418347608600
%N A290352 Euler transform of the Fubini numbers (ordered Bell numbers, A000670).
%H A290352 Alois P. Heinz, <a href="/A290352/b290352.txt">Table of n, a(n) for n = 0..424</a>
%F A290352 a(n) ~ n! / (2 * (log(2))^(n+1)). - _Vaclav Kotesovec_, May 31 2019
%p A290352 b:= proc(n, m) option remember;
%p A290352      `if`(n=0, m!, m*b(n-1, m)+b(n-1, m+1))
%p A290352     end:
%p A290352 a:= proc(n) option remember; `if`(n=0, 1, add(add(d*
%p A290352       b(d, 0), d=numtheory[divisors](j))*a(n-j), j=1..n)/n)
%p A290352     end:
%p A290352 seq(a(n), n=0..30);
%t A290352 b[n_, m_]:=b[n, m]=If[n==0, m!, Sum[b[n - 1, Max[m, j]], {j, m + 1}]]; a[n_]:=a[n]=If[n==0, 1, Sum[Sum[d*b[d, 0], {d, Divisors[j]}] a[n - j], {j, n}]/n]; Table[a[n], {n, 0, 50}] (* _Indranil Ghosh_, Jul 28 2017, after Maple code *)
%Y A290352 Cf. A000670, A007003, A095993, A290351.
%K A290352 nonn
%O A290352 0,3
%A A290352 _Alois P. Heinz_, Jul 28 2017