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