A305852 Weigh transform of the Fubini numbers (ordered Bell numbers, A000670).

1, 1, 3, 16, 91, 658, 5567, 54917, 620081, 7905592, 112382245, 1762646331, 30231516786, 562750751610, 11297034281595, 243241826522376, 5591075279423398, 136633359995403580, 3537193288612096901, 96697587673174195740, 2783492094736121087958

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..424

Formula

G.f.: Product_{k>=1} (1+x^k)^A000670(k).

a(n) ~ n! / (2 * log(2)^(n+1)). - Vaclav Kotesovec, Sep 10 2019

Maple

g:= proc(n) option remember; `if`(n=0, 1,
      add(g(n-j)*binomial(n, j), j=1..n))
    end:
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
      add(binomial(g(i), j)*b(n-i*j, i-1), j=0..n/i)))
    end:
a:= n-> b(n$2):
seq(a(n), n=0..30);

Mathematica

g[n_] := g[n] = If[n == 0, 1,
    Sum[g[n - j] Binomial[n, j], {j, 1, n}]];
b[n_, i_] := b[n, i] = If[n == 0, 1, If[i<1, 0,
    Sum[Binomial[g[i], j] b[n - i j, i - 1], {j, 0, n/i}]]];
a[n_] := b[n, n];
a /@ Range[0, 30] (* Jean-François Alcover, Dec 21 2020, after Alois P. Heinz *)

Crossrefs

Cf. A000670, A290352, A305850, A305853.

Sequence in context: A009124 A067679 A099952 * A221764 A371742 A213229

Adjacent sequences: A305849 A305850 A305851 * A305853 A305854 A305855

Keyword

nonn

Author

Alois P. Heinz, Jun 11 2018

Status

approved