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 A305031 #26 Jun 07 2023 20:05:51
%S A305031 1,6,18,44,102,228,500,1080,2310,4900,10332,21672,45276,94248,195624,
%T A305031 404976,836550,1724580,3549260,7293000,14965236,30669496,62783448,
%U A305031 128388624,262303132,535422888,1092063000,2225728400,4533175800,9226818000,18769219920,38158909920
%N A305031 Expansion of ((1 + 2*x)/(1 - 2*x))^(3/2).
%C A305031 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.
%H A305031 Seiichi Manyama, <a href="/A305031/b305031.txt">Table of n, a(n) for n = 0..3000</a>
%F A305031 n*a(n) = 6*a(n-1) + 4*(n-2)*a(n-2) for n > 1.
%F A305031 a(n) ~ 2^(n + 5/2) * sqrt(n/Pi). - _Vaclav Kotesovec_, May 28 2018
%t A305031 CoefficientList[Series[((1+2*x)/(1-2*x))^(3/2), {x,0,40}], x] (* _G. C. Greubel_, Jun 07 2023 *)
%o A305031 (PARI) N=66; x='x+O('x^N); Vec(((1+2*x)/(1-2*x))^(3/2))
%o A305031 (Magma) [n le 2 select 6^(n-1) else 2*(3*Self(n-1) + 2*(n-3)*Self(n-2))/(n-1): n in [1..40]]; // _G. C. Greubel_, Jun 07 2023
%o A305031 (SageMath)
%o A305031 @CachedFunction
%o A305031 def a(n): # b = A305031
%o A305031 if n<2: return 6^n
%o A305031 else: return 2*(3*a(n-1) + 2*(n-2)*a(n-2))//n
%o A305031 [a(n) for n in range(41)] # _G. C. Greubel_, Jun 07 2023
%Y A305031 ((1 + 2*x)/(1 - 2*x))^(m/2): A063886 (m=1), this sequence (m=3), A241204 (m=4).
%Y A305031 Cf. A304941, A305032.
%K A305031 nonn
%O A305031 0,2
%A A305031 _Seiichi Manyama_, May 24 2018