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 A186186 #20 Oct 30 2022 08:59:30
%S A186186 1,1,3,12,63,403,2919,22833,187799,1599718,13984383,124717327,
%T A186186 1130144932,10375309228,96290993853,901915801437,8514822062757,
%U A186186 80939662475426,774025387921462,7441380898249458,71879194326339456,697253570563306939,6789448668631285664,66340474776507262638
%N A186186 Expansion of 1/(1-x/(1-x)*A(x/(1-x))) where A(x) is the g.f. of A002293.
%H A186186 Andrew Howroyd, <a href="/A186186/b186186.txt">Table of n, a(n) for n = 0..500</a>
%H A186186 Vladimir Kruchinin and D. V. Kruchinin, <a href="http://arxiv.org/abs/1103.2582">Composita and their properties</a>, arXiv:1103.2582 [math.CO], 2011-2013.
%F A186186 a(n) = Sum_{m=1..n} Sum_{k=m..n} binomial(n-1,k-1)*m/(3*k-2*m)*binomial(4*k-3*m-1,k-m), n>0, a(0)=1.
%o A186186 (PARI) a(n)={if(n<1, n==0, sum(m=1, n, sum(k=m, n, binomial(n-1,k-1)*m/(3*k-2*m)*binomial(4*k-3*m-1,k-m))))} \\ _Andrew Howroyd_, Apr 17 2021
%Y A186186 Cf. A002293.
%K A186186 nonn
%O A186186 0,3
%A A186186 _Vladimir Kruchinin_, Feb 14 2011
%E A186186 Terms a(18) and beyond from _Andrew Howroyd_, Apr 17 2021