A290351 Euler transform of the Bell numbers (A000110).

1, 1, 3, 8, 26, 88, 340, 1411, 6417, 31474, 166242, 939646, 5659613, 36158227, 244049562, 1733702757, 12919475840, 100690425442, 818554392962, 6924577964036, 60828588178031, 553821749290234, 5217264062756556, 50776256646839085, 509823607380230570

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..576

Maple

b:= proc(n) option remember; `if`(n=0, 1, add(
      b(n-j)*binomial(n-1, j-1), j=1..n))
    end:
a:= proc(n) option remember; `if`(n=0, 1, add(add(d*
      b(d), d=numtheory[divisors](j))*a(n-j), j=1..n)/n)
    end:
seq(a(n), n=0..30);

Mathematica

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 *)

Crossrefs

Cf. A000110, A085686, A290352, A305850.

Sequence in context: A189177 A151444 A151458 * A148815 A148816 A148817

Adjacent sequences: A290348 A290349 A290350 * A290352 A290353 A290354

Keyword

nonn

Author

Alois P. Heinz, Jul 28 2017

Status

approved