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

0,1

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

Formula

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

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<k, A(k, n),
     `if`(k=0, b(n), (A(n+1, k-1)+add(A(n-k+j, j)
      *binomial(k-1, j), j=0..k-1)+A(n, k-1))/2))
    end:
a:= 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 *)

Crossrefs

Cf. A322765, A346500.

Sequence in context: A222080 A122708 A337012 * A292424 A225623 A005366

Adjacent sequences: A322764 A322765 A322766 * A322768 A322769 A322770

Keyword

nonn

Author

N. J. A. Sloane, Dec 30 2018

Status

approved