A384338 a(n) = Sum_{k=0..n} 2^k * binomial(3*n+1,k) * binomial(3*n-k,n-k).

1, 11, 169, 2864, 50857, 928091, 17242900, 324433064, 6162083161, 117893396513, 2268645170929, 43862498370812, 851378415887356, 16580151838496036, 323804481725009608, 6339277230341165264, 124372602047494986361, 2444709901233344894381

Offset

0,2

Links

Table of n, a(n) for n=0..17.

Formula

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

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

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

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

Prog

(PARI) a(n) = sum(k=0, n, 2^k*binomial(3*n+1, k)*binomial(3*n-k, n-k));

Crossrefs

Cf. A385320.

Sequence in context: A386869 A157944 A362501 * A233290 A167245 A331929

Adjacent sequences: A384335 A384336 A384337 * A384339 A384340 A384341

Keyword

nonn

Author

Seiichi Manyama, Aug 04 2025

Status

approved