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%I #20 Oct 30 2022 08:59:30
%S 1,1,3,12,63,403,2919,22833,187799,1599718,13984383,124717327,
%T 1130144932,10375309228,96290993853,901915801437,8514822062757,
%U 80939662475426,774025387921462,7441380898249458,71879194326339456,697253570563306939,6789448668631285664,66340474776507262638
%N Expansion of 1/(1-x/(1-x)*A(x/(1-x))) where A(x) is the g.f. of A002293.
%H Andrew Howroyd, <a href="/A186186/b186186.txt">Table of n, a(n) for n = 0..500</a>
%H 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 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 (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 Cf. A002293.
%K nonn
%O 0,3
%A _Vladimir Kruchinin_, Feb 14 2011
%E Terms a(18) and beyond from _Andrew Howroyd_, Apr 17 2021
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