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A290351 Euler transform of the Bell numbers (A000110).

%I A290351 #11 Jun 11 2018 18:30:26
%S A290351 1,1,3,8,26,88,340,1411,6417,31474,166242,939646,5659613,36158227,
%T A290351 244049562,1733702757,12919475840,100690425442,818554392962,
%U A290351 6924577964036,60828588178031,553821749290234,5217264062756556,50776256646839085,509823607380230570
%N A290351 Euler transform of the Bell numbers (A000110).
%H A290351 Alois P. Heinz, <a href="/A290351/b290351.txt">Table of n, a(n) for n = 0..576</a>
%p A290351 b:= proc(n) option remember; `if`(n=0, 1, add(
%p A290351       b(n-j)*binomial(n-1, j-1), j=1..n))
%p A290351     end:
%p A290351 a:= proc(n) option remember; `if`(n=0, 1, add(add(d*
%p A290351       b(d), d=numtheory[divisors](j))*a(n-j), j=1..n)/n)
%p A290351     end:
%p A290351 seq(a(n), n=0..30);
%t A290351 b[n_]:=b[n]=If[n==0, 1, Sum[b[n - j] Binomial[n - 1, j - 1], {j, n}]]; a[n_]:=a[n]=If[n==0, 1, Sum[Sum[d*b[d], {d, Divisors[j]}] a[n - j], {j, n}]/n]; Table[a[n], {n, 0, 50}] (* _Indranil Ghosh_, Jul 28 2017, after Maple code *)
%Y A290351 Cf. A000110, A085686, A290352, A305850.
%K A290351 nonn
%O A290351 0,3
%A A290351 _Alois P. Heinz_, Jul 28 2017