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A322771 Row 1 of array in A322770.

%I A322771 #12 Apr 29 2022 05:47:55
%S A322771 1,3,18,172,2295,40043,875936,23308546,737478487,27252363585,
%T A322771 1159335917625,56103737161197,3057787510932485,186102920689311261,
%U A322771 12555513437042340449,932964243520888524391,75926403820972271325522,6733532223196893844825456,647846856775383975668238328,67349524752043243630964385000
%N A322771 Row 1 of array in A322770.
%H A322771 Alois P. Heinz, <a href="/A322771/b322771.txt">Table of n, a(n) for n = 0..300</a>
%F A322771 a(n) = A346517(n,n+1) = A346517(n+1,n). - _Alois P. Heinz_, Jul 21 2021
%p A322771 b:= proc(n) option remember; `if`(n=0, 1,
%p A322771       add(b(n-j)*binomial(n-1, j-1), j=1..n))
%p A322771     end:
%p A322771 A:= proc(n, k) option remember; `if`(n<k, A(k, n),
%p A322771      `if`(k=0, b(n), (A(n+1, k-1)-add(A(n-k+j, j)
%p A322771       *binomial(k-1, j), j=0..k-1)+A(n, k-1))/2))
%p A322771     end:
%p A322771 a:= n-> A(n, n+1):
%p A322771 seq(a(n), n=0..19);  # _Alois P. Heinz_, Jul 21 2021
%t A322771 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}])];
%t A322771 a[n_] := Q[1, n];
%t A322771 Table[a[n], {n, 0, 19}] (* _Jean-François Alcover_, Apr 29 2022 *)
%Y A322771 Cf. A322770, A346517.
%K A322771 nonn
%O A322771 0,2
%A A322771 _N. J. A. Sloane_, Dec 30 2018