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%I #6 Aug 09 2017 12:14:21
%S 1,2,7,32,169,974,5947,37820,247885,1662890,11362399,78806936,
%T 553386097,3926523782,28108587139,202764451700,1472446595221,
%U 10755543924578,78973277044903,582558618222416,4315238786662585
%N Convolution of generalized Catalan numbers A064062 (called C(n;2)).
%C Row sums of triangle A115193, called C(1,2).
%C The o.g.f. given below follows from the Riordan matrix structure of the triangle A115193. See the o.g.f. for the row polynomials of A115193.
%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, after theorem 5.
%F a(n)= sum(A115193(n,m),m=0..n), n>=0.
%F G.f.: ((1+2*x*c(2*x))/(1+x))^2 = ((1-2*x) + 6*x*c(2*x))/(1+x)^2, with the o.g.f. c(x) of Catalan numbers A000108.
%F a(n)= sum(C(2;n-k)*C(2;k),k=0..n), n>=0, with C(2;n):= A064062(n).
%F a(n)=4*A178792(n)-3*(n+1)*A064062(n+1) [From _Joseph Abate_, Jun 21 2010]
%F n*a(n) +(-7*n+13)*a(n-1) +4*(-2*n+1)*a(n-2)=0. - _R. J. Mathar_, Aug 09 2017
%K nonn
%O 0,2
%A _Wolfdieter Lang_, Feb 23 2006