A227504 Schroeder triangle sums: a(n) = A006603(n+1) - A006318(n+1).

1, 4, 17, 74, 335, 1566, 7515, 36836, 183709, 929392, 4758477, 24611950, 128411643, 675051770, 3572165431, 19012868648, 101718917721, 546707554844, 2950563205705, 15983712882930, 86880753686279, 473710078493718, 2590187432233363, 14199709022579788

Offset: 1

Author

Johannes W. Meijer, Jul 15 2013

Keywords

• nonn
• easy

Comments

The terms of this sequence equal the Kn22 sums, see A180662, of the Schroeder triangle A033877 (with offset 1 and n for columns and k for rows).

Crossrefs

Cf. A033877, A006603, A006318, A227505.

Programs

Maple

A227504 := proc(n) local k, T; T := proc(n, k) option remember; if n=1 then return(1) fi; if kA227504(n), n = 1..24);
A227504 := proc(n): A006603(n+1) - A006318(n+1) end: A006603 := n -> add((k*add(binomial(n-k+2, i)*binomial(2*n-3*k-i+3, n-k+1), i= 0.. n-2*k+2)) / (n-k+2), k= 1.. n/2+1): A006318 := n -> add(binomial(n+k, n-k) * binomial(2*k, k)/(k+1), k=0..n): seq(A227504(n), n=1..24);

Formula

a(n) = sum(A033877(n-2*k+2, n-k+2), k=1..floor((n+1)/2)).

a(n) = A006603(n+1) - A006318(n+1).