A322767 Row 2 of array in A322765.

2, 11, 92, 1075, 16601, 325269, 7837862, 226700129, 7720099374, 304732680254, 13763771702539, 703691774091622, 40351866669219915, 2574830780826344436, 181574292457398520558, 14065771632972561098569, 1190588796562104776974207

Offset: 0

Author

N. J. A. Sloane, Dec 30 2018

Keywords

• nonn

References

• D. E. Knuth, The Art of Computer Programming, Vol. 4A, Table A-1, page 778.

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..300

Crossrefs

Cf. A322765, A346500.

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..22);  # Alois P. Heinz, Jul 21 2021

Mathematica

P[m_, n_] := P[m, n] = If[n == 0, BellB[m], (1/2)(P[m+2, n-1] + P[m+1, n-1] + Sum[Binomial[n-1, k] P[m, k], {k, 0, n-1}])];
a[n_] := P[2, n];
Table[a[n], {n, 0, 22}] (* Jean-François Alcover, Apr 29 2022 *)

Formula

a(n) = A346500(n,n+2) = A346500(n+2,n). - Alois P. Heinz, Jul 21 2021