A322772 Row 2 of array in A322770.

2, 9, 70, 801, 12347, 243235, 5908978, 172449180, 5925731200, 235946129714, 10745098631229, 553630279110396, 31978001903989065, 2054387367168242251, 145795148420558536232, 11361381129471379493270, 967044630942570464100761, 89483154423059719127570924, 8963545185499520505954151682

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+2):
seq(a(n), n=0..18);  # 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[2, n];
Table[a[n], {n, 0, 18}] (* Jean-François Alcover, Apr 29 2022 *)

Formula

a(n) = A346517(n,n+2) = A346517(n+2,n). - Alois P. Heinz, Jul 21 2021