A322769 Main diagonal of array in A322765.

1, 4, 92, 5133, 537813, 91914202, 23456071495, 8411911367949, 4055497274641836, 2540939492105630071, 2014322292658946180922, 1977121111959534634757742, 2360026677940190304494287625, 3374607252811005168634470847052, 5706308288951111509370981721908854

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..200

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(2*n, n):
seq(a(n), n=0..15);  # 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[n, n];
Table[a[n], {n, 0, 15}] (* Jean-François Alcover, Apr 29 2022 *)

Formula

a(n) = A346500(2n,n). - Alois P. Heinz, Jul 20 2021