A374599 Expansion of 1/sqrt(1 - 4*x - 8*x^4).

1, 2, 6, 20, 74, 276, 1044, 3992, 15414, 59948, 234484, 921432, 3634916, 14386248, 57097704, 227166384, 905714150, 3617851980, 14475452484, 58004111160, 232737175404, 934969613528, 3760157234584, 15137340947280, 60994657996476, 245980435701752

Offset: 0

Author

Seiichi Manyama, Jul 13 2024

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A360219, A360267.

Cf. A084609, A374598.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(1/sqrt(1-4*x-8*x^4))

PARI

a(n) = sum(k=0, n\4, 2^k*binomial(n-3*k, k)*binomial(2*(n-3*k), n-3*k));

Formula

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

n*a(n) = 2*(2*n-1)*a(n-1) + 4*(2*n-4)*a(n-4).