A386938 - OEIS

A386938

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

1, 6, 57, 608, 6835, 79170, 934892, 11189568, 135263799, 1647649850, 20191754297, 248664799344, 3074813151956, 38151145101048, 474747568376520, 5922579575399680, 74047774139941503, 927579860291591226, 11639480787978105179, 146278009406326705600, 1840856649159814801515

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

OFFSET

0,2

LINKS

Table of n, a(n) for n=0..20.

FORMULA

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

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

a(n) = Sum_{k=0..n} 2^k * (-1)^(n-k) * binomial(4*n+1,k) * binomial(3*n-k+1,n-k).

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

PROG

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