%I A048990
%S A048990 1,2,14,132,1430,16796,208012,2674440,35357670,477638700,6564120420,
%T A048990 91482563640,1289904147324,18367353072152,263747951750360,
%U A048990 3814986502092304,55534064877048198,812944042149730764
%N A048990 Catalan numbers with even index (A000108(2*n), n >= 0): a(n) = C(4*n,
               2*n)/(2*n+1).
%C A048990 With interpolated zeros, this is C(n)(1+(-1)^n)/2 with g.f. given by 
               2/(sqrt(1+4x)+sqrt(1-4x)). - Paul Barry (pbarry(AT)wit.ie), Sep 09 
               2004
%F A048990 G.f.: A(x) = sqrt(1/8*x^-1*(1-sqrt(1-16*x))).
%e A048990 sqrt(2*x^-1*(1-sqrt(1-x))) = 1 + 1/8*x + 7/128*x^2 + 33/1024*x^3 + ...
%o A048990 (Mupad) combinat::dyckWords::count(2*n) $ n = 0..28 - Zerinvary Lajos 
               (zerinvarylajos(AT)yahoo.com), Apr 14 2007
%Y A048990 Cf. A000108, A024492.
%Y A048990 Equals 2 * A065097.
%Y A048990 Cf. A000108.
%Y A048990 Sequence in context: A121082 A155650 A146971 this_sequence A089602 A052641 
               A157085
%Y A048990 Adjacent sequences: A048987 A048988 A048989 this_sequence A048991 A048992 
               A048993
%K A048990 easy,nonn
%O A048990 0,2
%A A048990 Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de)