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

0,2

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+1) = A346500(n+1,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+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 *)

Crossrefs

Cf. A322765, A346500.

Sequence in context: A210918 A052880 A090357 * A160886 A192546 A213438

Adjacent sequences: A322763 A322764 A322765 * A322767 A322768 A322769

Keyword

nonn

Author

N. J. A. Sloane, Dec 30 2018

Status

approved