A304940 - OEIS

%I #19 May 22 2018 09:54:58

%S 1,4,8,32,96,384,1280,5120,17920,71680,258048,1032192,3784704,

%T 15138816,56229888,224919552,843448320,3373793280,12745441280,

%U 50981765120,193730707456,774922829824,2958796259328,11835185037312,45368209309696,181472837238784

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

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

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

%H Seiichi Manyama, <a href="/A304940/b304940.txt">Table of n, a(n) for n = 0..1000</a>

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

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

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

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

%Y Cf. A063886.

%K nonn

%O 0,2

%A _Seiichi Manyama_, May 22 2018