A304940 Expansion of ((1 + 4*x)/(1 - 4*x))^(1/2).

1, 4, 8, 32, 96, 384, 1280, 5120, 17920, 71680, 258048, 1032192, 3784704, 15138816, 56229888, 224919552, 843448320, 3373793280, 12745441280, 50981765120, 193730707456, 774922829824, 2958796259328, 11835185037312, 45368209309696, 181472837238784

Offset: 0

Author

Seiichi Manyama, May 22 2018

Keywords

• nonn

Comments

Let ((1 + k*x)/(1 - k*x))^(m/k) = a(0) + a(1)*x + a(2)*x^2 + ...

Then n*a(n) = 2*m*a(n-1) + k^2*(n-2)*a(n-2) for n > 1.

Links

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

Crossrefs

((1 + 4*x)/(1 - 4*x))^(m/4): A303537 (m=1), this sequence (m=2), A304941 (m=3), A081654 (m=4).

Cf. A063886.

Programs

PARI

N=66; x='x+O('x^N); Vec(((1+4*x)/(1-4*x))^(1/2))

Formula

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

a(n) = 2^n * A063886(n).