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%I #17 Aug 08 2018 15:21:45
%S 1,1,3,13,62,317,1707,9529,54634,319838,1903895,11488985,70122538,
%T 432126645,2685003765,16802798157,105811579002,670008272170,
%U 4263402119458,27248174904238,174836857576628,1125847862614733,7273384212430489,47128196689500189
%N G.f. A(x) given by A(x) = 1+x*A(x)^2+x^2*A(x)^4+2*x^3*A(x)^6.
%H Vladimir Kruchinin, 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) = 1/(2*n-1)*sum(j=0..2*n-1, binomial(i=j..n+j-1, 2*n-1,j)*sum(binomial(j,i-j)*binomial(2*n-j-1,3*j-3*n-i+1)*2^(3*j-3*n-i+1))), n>0.
%t m = maxExponent = 20;
%t A[_] = 0;
%t Do[A[x_] = 1 + x A[x]^2 + x^2 A[x]^4 + 2 x^3 A[x]^6 + O[x]^m, {m}];
%t CoefficientList[A[x], x] (* _Jean-François Alcover_, Aug 08 2018 *)
%K nonn
%O 0,3
%A _Vladimir Kruchinin_, Feb 15 2011
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