A322771 Row 1 of array in A322770.

1, 3, 18, 172, 2295, 40043, 875936, 23308546, 737478487, 27252363585, 1159335917625, 56103737161197, 3057787510932485, 186102920689311261, 12555513437042340449, 932964243520888524391, 75926403820972271325522, 6733532223196893844825456, 647846856775383975668238328, 67349524752043243630964385000

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..300

Formula

a(n) = A346517(n,n+1) = A346517(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..19);  # Alois P. Heinz, Jul 21 2021

Mathematica

Q[m_, n_] := Q[m, n] = If[n == 0, BellB[m], (1/2)(Q[m+2, n-1] + Q[m+1, n-1] - Sum[Binomial[n-1, k] Q[m, k], {k, 0, n-1}])];
a[n_] := Q[1, n];
Table[a[n], {n, 0, 19}] (* Jean-François Alcover, Apr 29 2022 *)

Crossrefs

Cf. A322770, A346517.

Sequence in context: A367373 A289683 A193098 * A177447 A328031 A005192

Adjacent sequences: A322768 A322769 A322770 * A322772 A322773 A322774

Keyword

nonn

Author

N. J. A. Sloane, Dec 30 2018

Status

approved