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 A305612 #15 Nov 04 2020 13:35:28
%S A305612 0,3,9,22,51,114,250,540,1155,2450,5166,10836,22638,47124,97812,
%T A305612 202488,418275,862290,1774630,3646500,7482618,15334748,31391724,
%U A305612 64194312,131151566,267711444,546031500,1112864200,2266587900,4613409000,9384609960,19079454960
%N A305612 Expansion of 1/2 * (((1 + 2*x)/(1 - 2*x))^(3/2) - 1).
%C A305612 Let 1/2 * (((1 + k*x)/(1 - k*x))^(m/k) - 1) = a(0) + a(1)*x + a(2)*x^2 + ...
%C A305612 Then n*a(n) = 2*m*a(n-1) + k^2*(n-2)*a(n-2) for n > 1.
%H A305612 Seiichi Manyama, <a href="/A305612/b305612.txt">Table of n, a(n) for n = 0..3000</a>
%F A305612 n*a(n) = 6*a(n-1) + 4*(n-2)*a(n-2) for n > 1.
%F A305612 a(n) = A305031(n)/2 for n > 0.
%p A305612 seq(coeff(series((1/2)*(((1+2*x)/(1-2*x))^(3/2)-1), x,n+1),x,n),n=0..35); # _Muniru A Asiru_, Jun 06 2018
%t A305612 CoefficientList[Series[((((1+2x)/(1-2x))^(3/2))-1)/2,{x,0,40}],x] (* _Harvey P. Dale_, Nov 04 2020 *)
%Y A305612 1/2 * (((1 + 2*x)/(1 - 2*x))^(m/2) - 1): A001405(n-1) (m=1), this sequence (m=3).
%Y A305612 Cf. A305031.
%K A305612 nonn
%O A305612 0,2
%A A305612 _Seiichi Manyama_, Jun 06 2018