A305609 - OEIS

%I #19 Dec 30 2023 12:19:18

%S 0,1,1,22,43,862,2122,40012,111859,2016566,6130494,106709364,

%T 344744574,5831760108,19744810932,326100935448,1146472029123,

%U 18549990711078,67282629958006,1069313429135204,3982410828494666,62297616737399876,237367322452180556

%N Expansion of 1/2 * (((1 + 8*x)/(1 - 8*x))^(1/8) - 1).

%C Let 1/2 * (((1 + k*x)/(1 - k*x))^(m/k) - 1) = 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="/A305609/b305609.txt">Table of n, a(n) for n = 0..1000</a>

%F n*a(n) = 2*a(n-1) + 64*(n-2)*a(n-2) for n > 1.

%F a(n) = A303538(n)/2 for n > 0.

%p seq(coeff(series((1/2)*(((1+8*x)/(1-8*x))^(1/8)-1), x,30),x,n),n=0..25); # _Muniru A Asiru_, Jun 06 2018

%Y 1/2 * (((1 + k*x)/(1 - k*x))^(1/k) - 1): A001405(n-1) (k=2), A305608 (k=4), this sequence (k=8).

%Y Cf. A303538.

%K nonn

%O 0,4

%A _Seiichi Manyama_, Jun 06 2018