A383884 a(n) = Sum_{k=0..n} 2^k * binomial(2*n+1,k) * binomial(2*n-k,n-k).

1, 8, 76, 776, 8236, 89528, 989080, 11055248, 124659148, 1415338328, 16157960776, 185298481904, 2133004809976, 24631812347696, 285225658980016, 3310631101181216, 38506555289077516, 448698354100917656, 5236993294930652776, 61212903131657378096, 716430640316516361256

Offset: 0

Author

Seiichi Manyama, Aug 04 2025

Keywords

• nonn

Crossrefs

Cf. A385319.

Programs

PARI

a(n) = sum(k=0, n, 2^k*binomial(2*n+1, k)*binomial(2*n-k, n-k));

Formula

a(n) = [x^n] (1+2*x)^(2*n+1)/(1-x)^(n+1).

a(n) = [x^n] 1/((1-2*x) * (1-3*x)^(n+1)).

a(n) = Sum_{k=0..n} 3^k * (-1)^(n-k) * binomial(2*n+1,k).

a(n) = Sum_{k=0..n} 3^k * 2^(n-k) * binomial(n+k,k).