A383716 - OEIS

A383716

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

1, 9, 127, 2001, 33151, 565249, 9819391, 172826369, 3071424511, 54992986113, 990477877247, 17925526679553, 325710362673151, 5938147061596161, 108571788661555199, 1990032340043366401, 36554697970011340799, 672749920475758460929, 12402180156683794251775

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

OFFSET

0,2

LINKS

Table of n, a(n) for n=0..18.

FORMULA

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

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

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

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

PROG

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