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%I #4 Oct 25 2012 14:30:48
%S 1,2,4,10,24,62,156,408,1048,2758,7164,18922,49488,131016,344208,
%T 912720,2405496,6385814,16868604,44818494,118595064,315299694,
%U 835423164,2222185344,5894038944,15684059112
%N Row sums of the Riordan array (1/(1+x),x(1+2x)/(1+x)^3)^(-1).
%C A transform of 2^n by the Riordan array (1,x(1-x^2))^(-1).
%C (1/(1+x),x(1+2x)/(1+x)^3)^(-1) factors as (1,x(1-x^2))^(-1)*(1/(1-x),x/(1-x)).
%C Hankel transform is A138176.
%F G.f.: 1/(1-2v) where v=(2/sqrt(3))*sin(asin(x*3*sqrt(3)/2)/3), the reversion of x(1-x^2);
%F Conjecture: 12*n*(n-1)*(39*n-88)*a(n) -8*(n-1)*(156*n^2-352*n+27)*a(n-1) +9*(-351*n^3-2196*n^2-4325*n+2680)*a(n-2) +24*(39*n-49)*(3*n-7)*(3*n-8)*a(n-3)=0.- _R. J. Mathar_, Oct 25 2012
%K easy,nonn
%O 0,2
%A _Paul Barry_, Mar 03 2008
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