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A322771 Row 1 of array in A322770. 3
1, 3, 18, 172, 2295, 40043, 875936, 23308546, 737478487, 27252363585, 1159335917625, 56103737161197, 3057787510932485, 186102920689311261, 12555513437042340449, 932964243520888524391, 75926403820972271325522, 6733532223196893844825456, 647846856775383975668238328, 67349524752043243630964385000 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois Alcover, Apr 29 2022 *)

CROSSREFS

Cf. A322770, A346517.

Sequence in context: A113130 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

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Last modified September 26 14:21 EDT 2022. Contains 356999 sequences. (Running on oeis4.)