This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A305609 #19 Dec 30 2023 12:19:18 %S A305609 0,1,1,22,43,862,2122,40012,111859,2016566,6130494,106709364, %T A305609 344744574,5831760108,19744810932,326100935448,1146472029123, %U A305609 18549990711078,67282629958006,1069313429135204,3982410828494666,62297616737399876,237367322452180556 %N A305609 Expansion of 1/2 * (((1 + 8*x)/(1 - 8*x))^(1/8) - 1). %C A305609 Let 1/2 * (((1 + k*x)/(1 - k*x))^(m/k) - 1) = a(0) + a(1)*x + a(2)*x^2 + ... %C A305609 Then n*a(n) = 2*m*a(n-1) + k^2*(n-2)*a(n-2) for n > 1. %H A305609 Seiichi Manyama, <a href="/A305609/b305609.txt">Table of n, a(n) for n = 0..1000</a> %F A305609 n*a(n) = 2*a(n-1) + 64*(n-2)*a(n-2) for n > 1. %F A305609 a(n) = A303538(n)/2 for n > 0. %p A305609 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 A305609 1/2 * (((1 + k*x)/(1 - k*x))^(1/k) - 1): A001405(n-1) (k=2), A305608 (k=4), this sequence (k=8). %Y A305609 Cf. A303538. %K A305609 nonn %O A305609 0,4 %A A305609 _Seiichi Manyama_, Jun 06 2018