%I #14 Dec 17 2019 05:36:19
%S 1,1,2,5,16,58,222,869,3438,13672,54518,217706,870036,3478446,
%T 13910128,55632657,222513784,890019102,3559999490,14239834188,
%U 56958988812,227835217794,911339311462,3645353954182,14581408883620
%N Main diagonal of symmetric array defined by the recurrence T(n,1)=1, T(1,k)=1, for n >= k: T(n,k) = Sum_{i=1..k-1} T(n-i,k), for n < k: T(n,k) = Sum_{i=1..n-1} T(k-i,n).
%C a(n) mod 2 = A023900(n) mod 2. The recurrence mentioned in the title is the same as the recurrence in array A191898 but without the minus signs.
%F Main diagonal of array defined by: T(n,1)=1, T(1,k)=1, n >= k: Sum_{i=1..k-1} T(n-i,k), n < k: Sum_{i=1..n-1} T(k-i,n).
%t Clear[nn, t, n, k]; nn = 25;t[n_, 1] = 1;t[1, k_] = 1;t[n_, k_] := t[n, k] = If[n >= k, Sum[t[n - i, k], {i, 1, k - 1}], Sum[t[k - i, n], {i, 1, n - 1}]]; Table[t[n, n], {n, 1, nn}]
%Y Cf. A023900, A191898.
%K nonn
%O 1,3
%A _Mats Granvik_, May 12 2012