A129368 a(n) = Sum_{k=floor((n+1)/2)..n} binomial(2*k,k).

1, 2, 8, 26, 96, 342, 1266, 4678, 17548, 66098, 250854, 956034, 3660190, 14059866, 54176466, 209290554, 810370944, 3143964294, 12219099594, 47564314774, 185410843594, 723668533278, 2827767496998, 11061197519166

Offset: 0

Author

Paul Barry, Apr 11 2007

Keywords

• easy
• nonn

Comments

Partial sums of A129369.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A129369.

Programs

Magma

[(&+[Binomial(2*(n-k),n-k): k in [0..Floor(n/2)]]): n in [0..60]]; // G. C. Greubel, Jan 31 2024

Mathematica

Table[Sum[Binomial[2k,k],{k,Floor[(n+1)/2],n}],{n,0,30}] (* Harvey P. Dale, Aug 13 2012 *)

SageMath

[sum(binomial(2*(n-k),n-k) for k in range(1+(n//2))) for n in range(61)] # G. C. Greubel, Jan 31 2024

Formula

G.f.: (1/(1-x))*( 1/sqrt(1-4*x) - x/sqrt(1-4*x^2) ).

a(n) = Sum_{k=0..floor(n/2)} C(2*(n-k), n-k).