%I A067336
%S A067336 1,2,8,34,148,652,2892,12882,57540,257500,1153888,5175700,23231864,
%T A067336 104335376,468766292,2106773874,9470787588,42583186476,191494694352,
%U A067336 861248485884,3873850923288,17425765034376,78391476387672
%N A067336 a(0)=1, a(1)=2, a(n)=a(n-1)*9/2-Catalan(n-1) where Catalan(n)=C(2n,n)/
               (n+1)=A000108(n).
%C A067336 Note that while a(n) is even (for n>0), it is not a multiple of 4 only 
               when n=2^m-1, i.e. when Catalan(n) is odd.
%C A067336 Apply the Riordan matrix ((1+sqrt(1-4x))/2,(1-sqrt(1-4x))/2) (inverse 
               of (1/(1-x),x(1-x)) to 3^n. - Paul Barry (pbarry(AT)wit.ie), Mar 
               12 2005
%F A067336 a(n) =A067337(2n, n)
%F A067336 G.f.: (1+sqrt(1-4x))/(3sqrt(1-4x)-1); - Paul Barry (pbarry(AT)wit.ie), 
               Mar 12 2005
%F A067336 a(n)=Sum_[k, 0<=k<=n}A039599(n,k)*A001045(k+1). - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), 
               Jun 10 2007
%e A067336 a(2)=2*9/2-1=8; a(3)=8*9/2-2=34; a(4)=34*9/2-5=148; a(5)=148*9/2-14=652.
%Y A067336 Cf. A088218.
%Y A067336 Sequence in context: A014445 A113440 A034999 this_sequence A151829 A026387 
               A085362
%Y A067336 Adjacent sequences: A067333 A067334 A067335 this_sequence A067337 A067338 
               A067339
%K A067336 nonn
%O A067336 0,2
%A A067336 Henry Bottomley (se16(AT)btinternet.com), Jan 15 2002