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%I #8 May 25 2021 10:30:40
%S 1,2,9,58,446,3792,34369,325538,3184206,31917772,326156474,3385065348,
%T 35585008816,378116619692,4054571715729,43820012675698,
%U 476830454211926,5219833626494412,57444768682580494,635176593108262028
%N Convolution of generalized Catalan sequence A064063 (named C(3;n)).
%C Row sums of generalized Catalan triangle A116866 (named C(1,3)).
%H J. Abate, W. Whitt, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL14/Whitt/whitt6.html">Brownian Motion and the Generalized Catalan Numbers</a>, J. Int. Seq. 14 (2011) # 11.2.6, example after (34).
%F a(n)=sum(A116866(n,m),m=0..n), n>=0.
%F G.f.: ((1+3*x*c(3*x)/2)/(1+x/2))^2 = (4-3*x + 15*x*c(3*x))/(2+x)^2, with the o.g.f. c(x) of A000108 (Catalan numbers).
%F a(n)= sum(C(3;n-k)*C(3;k),k=0..n), n>=0, with C(3;n):= A064063(n).
%F 2*n*a(n) +(-23*n+37)*a(n-1) +6*(-2*n+1)*a(n-2)=0. - _R. J. Mathar_, Aug 09 2017
%K nonn,easy
%O 0,2
%A _Wolfdieter Lang_, Mar 24 2006
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