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A227791 Central terms of the triangle in A227550.

%I A227791 #27 Nov 03 2022 11:25:08
%S A227791 1,2,8,36,176,940,5568,37128,280992,2410812,23250080,249164344,
%T A227791 2934303264,37617633976,521009920256,7748175156240,123095897716800,
%U A227791 2080205257723740,37253560076385120,704703668205036120,14039778681732928800,293831851498842784680
%N A227791 Central terms of the triangle in A227550.
%F A227791 a(n) = A074911(2*n,n).
%p A227791 b:= proc(x, y) option remember; `if`(x=0, y!,
%p A227791       b(x-1, y)+b(sort([x, y-1])[]))
%p A227791     end:
%p A227791 a:= n-> b(n$2):
%p A227791 seq(a(n), n=0..26);  # _Alois P. Heinz_, Jul 14 2021
%t A227791 T[n_, 0] := n!; T[n_, n_] := n!;
%t A227791 T[n_, k_] /; 0<k<n := T[n, k] = T[n-1, k-1]+T[n-1, k];
%t A227791 a[n_] := T[2n, n];
%t A227791 Table[a[n], {n, 0, 21}] (* _Jean-François Alcover_, Nov 03 2022 *)
%o A227791 (Haskell)
%o A227791 a227791 n = a227550 (2 * n) n
%Y A227791 Cf. A074911, A225621, A227550.
%K A227791 nonn
%O A227791 0,2
%A A227791 _Reinhard Zumkeller_, Aug 05 2013