A322771 Row 1 of array in A322770.

1, 3, 18, 172, 2295, 40043, 875936, 23308546, 737478487, 27252363585, 1159335917625, 56103737161197, 3057787510932485, 186102920689311261, 12555513437042340449, 932964243520888524391, 75926403820972271325522, 6733532223196893844825456, 647846856775383975668238328, 67349524752043243630964385000

Offset: 0

Author

N. J. A. Sloane, Dec 30 2018

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..300

Crossrefs

Cf. A322770, A346517.

Programs

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, k) option remember; `if`(n A(n, n+1):
seq(a(n), n=0..19);  # Alois P. Heinz, Jul 21 2021

Mathematica

Q[m_, n_] := Q[m, n] = If[n == 0, BellB[m], (1/2)(Q[m+2, n-1] + Q[m+1, n-1] - Sum[Binomial[n-1, k] Q[m, k], {k, 0, n-1}])];
a[n_] := Q[1, n];
Table[a[n], {n, 0, 19}] (* Jean-François Alcover, Apr 29 2022 *)

Formula

a(n) = A346517(n,n+1) = A346517(n+1,n). - Alois P. Heinz, Jul 21 2021