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A322772 Row 2 of array in A322770.

%I A322772 #12 Apr 29 2022 05:47:49
%S A322772 2,9,70,801,12347,243235,5908978,172449180,5925731200,235946129714,
%T A322772 10745098631229,553630279110396,31978001903989065,2054387367168242251,
%U A322772 145795148420558536232,11361381129471379493270,967044630942570464100761,89483154423059719127570924,8963545185499520505954151682
%N A322772 Row 2 of array in A322770.
%H A322772 Alois P. Heinz, <a href="/A322772/b322772.txt">Table of n, a(n) for n = 0..300</a>
%F A322772 a(n) = A346517(n,n+2) = A346517(n+2,n). - _Alois P. Heinz_, Jul 21 2021
%p A322772 b:= proc(n) option remember; `if`(n=0, 1,
%p A322772       add(b(n-j)*binomial(n-1, j-1), j=1..n))
%p A322772     end:
%p A322772 A:= proc(n, k) option remember; `if`(n<k, A(k, n),
%p A322772      `if`(k=0, b(n), (A(n+1, k-1)-add(A(n-k+j, j)
%p A322772       *binomial(k-1, j), j=0..k-1)+A(n, k-1))/2))
%p A322772     end:
%p A322772 a:= n-> A(n, n+2):
%p A322772 seq(a(n), n=0..18);  # _Alois P. Heinz_, Jul 21 2021
%t A322772 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 A322772 a[n_] := Q[2, n];
%t A322772 Table[a[n], {n, 0, 18}] (* _Jean-François Alcover_, Apr 29 2022 *)
%Y A322772 Cf. A322770, A346517.
%K A322772 nonn
%O A322772 0,1
%A A322772 _N. J. A. Sloane_, Dec 30 2018