A098507 Diagonal sums of the number triangle A098505.

1, 1, 2, 2, 5, 6, 10, 9, 19, 22, 65, 88, 114, 187, 395, 376, 888, 520, 2645, 2017, 3303, 3590, 8820, 9408, 5785, 7792, 24181, 27047, 74720, 68731, 153394, 159394, 369957, 1261522, 4326030, 4924898, 6538595, 9754155, 10068484, 10541264, 24936678

Offset: 0

Author

Paul Barry, Sep 11 2004

Keywords

• easy
• nonn

Crossrefs

Cf. A098505.

Programs

Mathematica

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 *)

Formula

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