%I #7 Jun 19 2021 09:54:04

%S 1,1,2,2,5,6,10,9,19,22,65,88,114,187,395,376,888,520,2645,2017,3303,

%T 3590,8820,9408,5785,7792,24181,27047,74720,68731,153394,159394,

%U 369957,1261522,4326030,4924898,6538595,9754155,10068484,10541264,24936678

%N Diagonal sums of the number triangle A098505.

%F a(n) = Sum_{k=0..floor(n/2)} numerator((n-k+1)*binomial(n-k, k)/binomial(2*n-2*k, n-k)).

%t Table[Sum[Numerator[(n-k+1) Binomial[n-k,k]/Binomial[2n-2k,n-k]],{k,0,Floor[ n/2]}],{n,0,60}] (* _Harvey P. Dale_, Jun 19 2021 *)

%Y Cf. A098505.

%K easy,nonn

%O 0,3

%A _Paul Barry_, Sep 11 2004