A227791 - OEIS

%I #27 Nov 03 2022 11:25:08

%S 1,2,8,36,176,940,5568,37128,280992,2410812,23250080,249164344,

%T 2934303264,37617633976,521009920256,7748175156240,123095897716800,

%U 2080205257723740,37253560076385120,704703668205036120,14039778681732928800,293831851498842784680

%N Central terms of the triangle in A227550.

%F a(n) = A074911(2*n,n).

%p b:= proc(x, y) option remember; `if`(x=0, y!,

%p       b(x-1, y)+b(sort([x, y-1])[]))

%p     end:

%p a:= n-> b(n$2):

%p seq(a(n), n=0..26);  # _Alois P. Heinz_, Jul 14 2021

%t T[n_, 0] := n!; T[n_, n_] := n!;

%t T[n_, k_] /; 0<k<n := T[n, k] = T[n-1, k-1]+T[n-1, k];

%t a[n_] := T[2n, n];

%t Table[a[n], {n, 0, 21}] (* _Jean-François Alcover_, Nov 03 2022 *)

%o (Haskell)

%o a227791 n = a227550 (2 * n) n

%Y Cf. A074911, A225621, A227550.

%K nonn

%O 0,2

%A _Reinhard Zumkeller_, Aug 05 2013