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A322767 Row 2 of array in A322765.

%I A322767 #16 Apr 29 2022 05:47:17
%S A322767 2,11,92,1075,16601,325269,7837862,226700129,7720099374,304732680254,
%T A322767 13763771702539,703691774091622,40351866669219915,2574830780826344436,
%U A322767 181574292457398520558,14065771632972561098569,1190588796562104776974207
%N A322767 Row 2 of array in A322765.
%D A322767 D. E. Knuth, The Art of Computer Programming, Vol. 4A, Table A-1, page 778.
%H A322767 Seiichi Manyama, <a href="/A322767/b322767.txt">Table of n, a(n) for n = 0..300</a>
%F A322767 a(n) = A346500(n,n+2) = A346500(n+2,n). - _Alois P. Heinz_, Jul 21 2021
%p A322767 b:= proc(n) option remember; `if`(n=0, 1,
%p A322767       add(b(n-j)*binomial(n-1, j-1), j=1..n))
%p A322767     end:
%p A322767 A:= proc(n, k) option remember; `if`(n<k, A(k, n),
%p A322767      `if`(k=0, b(n), (A(n+1, k-1)+add(A(n-k+j, j)
%p A322767       *binomial(k-1, j), j=0..k-1)+A(n, k-1))/2))
%p A322767     end:
%p A322767 a:= n-> A(n, n+2):
%p A322767 seq(a(n), n=0..22);  # _Alois P. Heinz_, Jul 21 2021
%t A322767 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}])];
%t A322767 a[n_] := P[2, n];
%t A322767 Table[a[n], {n, 0, 22}] (* _Jean-François Alcover_, Apr 29 2022 *)
%Y A322767 Cf. A322765, A346500.
%K A322767 nonn
%O A322767 0,1
%A A322767 _N. J. A. Sloane_, Dec 30 2018