A322769 Main diagonal of array in A322765.

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

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..200

Formula

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

Crossrefs

Cf. A322765, A346500.

Sequence in context: A003737 A362511 A265238 * A012071 A012217 A012135

Adjacent sequences: A322766 A322767 A322768 * A322770 A322771 A322772

Keyword

nonn

Author

N. J. A. Sloane, Dec 30 2018

Status

approved