%I #12 Oct 30 2022 11:03:42
%S 1,2,1,14,4,1,134,32,6,1,1482,324,54,8,1,17818,3696,578,80,10,1,
%T 226214,45316,6810,904,110,12,1,2984206,583152,85278,11008,1310,144,
%U 14,1,40503890,7769348,1113854,140936,16490,1804,182,16,1,561957362,106250144,15004746,1870352,216002,23472,2394,224,18,1
%N Triangle T(n,k) for A(x)^k=sum(n>=k T(n,k)*x^n), where o.g.f. A(x) satisfies A(x)=(1+x*A(x)^3)/(1-x*A(x)^3),
%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 T(n,k):=k/(3*n-2*k)*sum(i=0..n-k, binomial(3*n-2*k,n-k-i)*binomial(3*n-2*k+i-1,3*n-2*k-1)), n>=k>0.
%o (Maxima)
%o T(n,k):=k/(3*n-2*k)*sum(binomial(3*n-2*k,n-k-i)*binomial(3*n-2*k+i-1,3*n-2*k-1),i,0,n-k);
%K nonn,tabl
%O 1,2
%A _Vladimir Kruchinin_, Mar 16 2011