A386867 - OEIS

A386867

a(n) = Sum_{k=0..n} 2^(n-k) * binomial(4*n+2,k) * binomial(4*n-k-1,n-k).

1, 12, 249, 5842, 144636, 3690840, 96028606, 2532467934, 67454242092, 1810467982144, 48887478311673, 1326582594222918, 36143786784056716, 988134308856642048, 27093384379207568028, 744735869371387679158, 20516019688758402141372, 566266846186568482197840

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

LINKS

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

FORMULA

a(n) = [x^n] (1+x)^(4*n+2)/(1-2*x)^(3*n).

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

a(n) = Sum_{k=0..n} 3^k * (-2)^(n-k) * binomial(4*n+2,k) * binomial(n-k+2,n-k).

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

PROG

(PARI) a(n) = sum(k=0, n, 2^(n-k)*binomial(4*n+2, k)*binomial(4*n-k-1, n-k));