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 A361814 #16 Mar 25 2023 12:07:41
%S A361814 1,2,16,100,660,4482,30886,215364,1515000,10730800,76426846,546792056,
%T A361814 3926775646,28290272420,204375145480,1479963148220,10739326203132,
%U A361814 78072933869364,568503202324540,4145718464390120,30271771382355430,221305746414518180
%N A361814 Expansion of 1/sqrt(1 - 4*x*(1+x)^5).
%H A361814 Winston de Greef, <a href="/A361814/b361814.txt">Table of n, a(n) for n = 0..1139</a>
%F A361814 a(n) = Sum_{k=0..n} binomial(2*k,k) * binomial(5*k,n-k).
%F A361814 n*a(n) = 2 * ( (2*n-1)*a(n-1) + 5*(2*n-2)*a(n-2) + 10*(2*n-3)*a(n-3) + 10*(2*n-4)*a(n-4) + 5*(2*n-5)*a(n-5) + (2*n-6)*a(n-6) ) for n > 5.
%o A361814 (PARI) my(N=30, x='x+O('x^N)); Vec(1/sqrt(1-4*x*(1+x)^5))
%o A361814 (PARI) a(n)= sum(k=0, n, binomial(2*k,k) * binomial(5*k,n-k)) \\ _Winston de Greef_, Mar 25 2023
%Y A361814 Cf. A006139, A137635, A360133, A361790, A361791, A361792, A361812, A361813.
%K A361814 nonn
%O A361814 0,2
%A A361814 _Seiichi Manyama_, Mar 25 2023