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 A360083 #12 Jul 13 2025 15:06:26
%S A360083 1,1,7,35,189,1092,6538,40278,253730,1626858,10582616,69669273,
%T A360083 463319257,3107941405,21004392887,142882885210,977562617826,
%U A360083 6722361860888,46438235933700,322111000796428,2242538435656450,15665017062799230,109761527468995102
%N A360083 a(n) = Sum_{k=0..n} binomial(5*k,n-k) * Catalan(k).
%H A360083 Harvey P. Dale, <a href="/A360083/b360083.txt">Table of n, a(n) for n = 0..1000</a>
%F A360083 G.f. A(x) satisfies A(x) = 1/(1 - x * (1+x)^5 * A(x)).
%F A360083 G.f.: 2 / (1 + sqrt( 1 - 4*x*(1+x)^5 )).
%t A360083 Table[Sum[Binomial[5k,n-k]CatalanNumber[k],{k,0,n}],{n,0,30}] (* _Harvey P. Dale_, Jul 13 2025 *)
%o A360083 (PARI) a(n) = sum(k=0, n, binomial(5*k, n-k)*binomial(2*k, k)/(k+1));
%o A360083 (PARI) my(N=30, x='x+O('x^N)); Vec(2/(1+sqrt(1-4*x*(1+x)^5)))
%Y A360083 Cf. A052709, A073155, A360076, A360082.
%Y A360083 Cf. A000108, A360090.
%K A360083 nonn
%O A360083 0,3
%A A360083 _Seiichi Manyama_, Jan 25 2023