A322766 Row 1 of array in A322765.

1, 4, 26, 249, 3274, 56135, 1207433, 31638625, 987249425, 36030130677, 1515621707692, 72603595393584, 3920675798922189, 236615520916677436, 15840357595697061964, 1168697367186883073296, 94486667847573203169757, 8328527812527985862657297, 796762955545266206229493979

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+1):
seq(a(n), n=0..22);  # Alois P. Heinz, Jul 21 2021

Mathematica

b[n_] := b[n] = If[n == 0, 1,
     Sum[b[n - j]*Binomial[n-1, j-1], {j, 1, n}]];
A[n_, k_] := A[n, k] = If[n < k, A[k, n],
     If[k == 0, b[n], (A[n+1, k - 1] + Sum[A[n - k + j, j]*
     Binomial[k-1, j], {j, 0, k - 1}] + A[n, k - 1])/2]];
a[n_] := A[n, n + 1];  Table[a[n], {n, 0, 22}] (* Jean-François Alcover, Jun 01 2022, after Alois P. Heinz *)

Formula

a(n) = A346500(n,n+1) = A346500(n+1,n). - Alois P. Heinz, Jul 21 2021