Search: id:A115197
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%I A115197
%S A115197 1,2,7,32,169,974,5947,37820,247885,1662890,11362399,78806936,553386097,
%T A115197 3926523782,28108587139,202764451700,1472446595221,10755543924578,
%U A115197 78973277044903,582558618222416,4315238786662585
%N A115197 Convolution of generalized Catalan numbers A064062 (called C(n;2)).
%C A115197 Row sums of triangle A115193, called C(1,2).
%C A115197 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.
%F A115197 a(n)= sum(A115193(n,m),m=0..n), n>=0.
%F A115197 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 A115197 a(n)= sum(C(2;n-k)*C(2;k),k=0..n), n>=0, with C(2;n):= A064062(n).
%Y A115197 Sequence in context: A047850 A108524 A006781 this_sequence A107593 A125277 
               A161392
%Y A115197 Adjacent sequences: A115194 A115195 A115196 this_sequence A115198 A115199 
               A115200
%K A115197 nonn
%O A115197 0,2
%A A115197 Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Feb 23 
               2006

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