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 A361816 #12 Mar 28 2023 10:48:26
%S A361816 1,2,0,-10,-22,12,174,344,-354,-3304,-5780,9180,65258,99132,-226620,
%T A361816 -1313580,-1690990,5441340,26681700,28070100,-128211552,-543818824,
%U A361816 -440381780,2978145240,11080939914,6162798092,-68377892976,-225107280388,-64286124152
%N A361816 Expansion of 1/sqrt(1 - 4*x*(1-x)^3).
%H A361816 Seiichi Manyama, <a href="/A361816/b361816.txt">Table of n, a(n) for n = 0..1000</a>
%F A361816 a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(2*k,k) * binomial(3*k,n-k).
%F A361816 n*a(n) = 2 * ( (2*n-1)*a(n-1) - 3*(2*n-2)*a(n-2) + 3*(2*n-3)*a(n-3) - (2*n-4)*a(n-4) ) for n > 3.
%o A361816 (PARI) my(N=30, x='x+O('x^N)); Vec(1/sqrt(1-4*x*(1-x)^3))
%Y A361816 Column k=3 of A361834.
%Y A361816 Cf. A085362, A110170, A162478, A359489, A359758, A360132, A361815, A361817.
%Y A361816 Cf. A361812.
%K A361816 sign
%O A361816 0,2
%A A361816 _Seiichi Manyama_, Mar 25 2023