A375276 Expansion of 1/sqrt(1 - 4*x - 8*x^3 + 4*x^4).

1, 2, 6, 24, 92, 360, 1448, 5888, 24144, 99744, 414432, 1729920, 7249088, 30476416, 128487552, 543014912, 2299764992, 9758138880, 41473582592, 176530905088, 752401603584, 3210723420160, 13716154361856, 58653842276352, 251049168687104, 1075442759868416

Offset: 0

Author

Seiichi Manyama, Aug 09 2024

Keywords

• nonn

Crossrefs

Cf. A108485.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(1/sqrt(1-4*x-8*x^3+4*x^4))

PARI

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

Formula

n * a(n) = 2*(2*n-1)*a(n-1) + 4*(2*n-3)*a(n-3) - 4*(n-2)*a(n-4).

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