A376809 Expansion of 1/sqrt(1 - 4*x^3/(1 - x)^2).
1, 0, 0, 2, 4, 6, 14, 34, 72, 154, 346, 774, 1714, 3822, 8574, 19238, 43204, 97254, 219286, 494962, 1118502, 2530522, 5730762, 12989634, 29467718, 66901378, 151996338, 345556218, 786092266, 1789284762, 4074927962, 9284968682, 21166439112, 48273612954, 110142596298
Offset: 0
Programs
-
PARI
my(N=40, x='x+O('x^N)); Vec(1/sqrt(1-4*x^3/(1-x)^2)) -
PARI
a(n) = sum(k=0, n\3, binomial(2*k,k) * binomial(n-k-1,n-3*k));
Formula
a(n) = Sum_{k=0..floor(n/3)} binomial(2*k,k) * binomial(n-k-1,n-3*k).