%I A076025
%S A076025 1,1,5,26,137,726,3858,20532,109361,582782,3106550,16562668,88314634,470942044,
%T A076025 2511443268,13393472616,71428622337,380940866574,2031641406798,10835261623356,
%U A076025 57787472903502,308197667445204,1643712737618748,8766437439778776,46754218658948922
%N A076025 G.f.: (1-3*x*C)/(1-4*x*C) where C = (1/2-1/2*(1-4*x)^(1/2))/x = g.f. 
               for Catalan numbers A000108.
%C A076025 Contribution from Paul Barry (pbarry(AT)wit.ie), Sep 23 2009: (Start)
%C A076025 The Hankel transform of this sequence is 3n+1 or 1,4,7,10,... (A016777).
%C A076025 The Hankel transform of the aeration of this sequence is A016777 doubled, 
               that is, 1,1,4,4,7,7,...
%C A076025 In general, the Hankel transform of [x^n](1-r*xc(x))/(1-(r+1)*xc(x)) 
               is rn+1, and that of the
%C A076025 corresponding aerated sequence is the doubled sequence of rn+1. (End)
%F A076025 a(n+1)=sum{k=0..n, 3^k*comb(2n+1, n-k)2(k+1)/(n+k+2)} - Paul Barry (pbarry(AT)wit.ie), 
               Jun 22 2004
%F A076025 a(n+1)=Sum_{k, 0<=k<=n}A039598(n,k)*3^k . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), 
               Mar 21 2007
%F A076025 a(n) = Sum_{k, 0<=k<=n}A039599(n,k)*A015518(k), for n>=1 . - Philippe 
               DELEHAM (kolotoko(AT)wanadoo.fr), Nov 22 2007
%Y A076025 Cf. A000108, A001700, A049027, A076026.
%Y A076025 Sequence in context: A052918 A018903 A083331 this_sequence A161731 A049607 
               A035029
%Y A076025 Adjacent sequences: A076022 A076023 A076024 this_sequence A076026 A076027 
               A076028
%K A076025 nonn
%O A076025 0,3
%A A076025 N. J. A. Sloane (njas(AT)research.att.com), Oct 29 2002