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A187887 Riordan matrix (1/((1-x)*sqrt(1-4*x)),x/(1-x)).

%I A187887 #15 Jun 23 2013 17:45:49
%S A187887 1,3,1,9,4,1,29,13,5,1,99,42,18,6,1,351,141,60,24,7,1,1275,492,201,84,
%T A187887 31,8,1,4707,1767,693,285,115,39,9,1,17577,6474,2460,978,400,154,48,
%U A187887 10,1,66197,24051,8934,3438,1378,554,202,58,11,1,250953,90248,32985,12372,4816,1932,756,260,69,12,1
%N A187887 Riordan matrix (1/((1-x)*sqrt(1-4*x)),x/(1-x)).
%C A187887 Row sums are A082590.
%C A187887 First column is A006134.
%F A187887 a(n,k) = [x^n] 1/((1-x)*sqrt(1-4*x))*(x/(1-x))^k.
%F A187887 Recurrence: a(n+1,k+1) = a(n,k+1) + a(n,k).
%F A187887 a(n,k) = sum(binomial(n-i,k)*binomial(2*i,i),i=0..n).
%F A187887 G.f.: 1/(sqrt(1-4*x)*(1-x-x*y)).
%e A187887 Triangle begins:
%e A187887 1,
%e A187887 3,1,
%e A187887 9,4,1,
%e A187887 29,13,5,1,
%e A187887 99,42,18,6,1,
%e A187887 351,141,60,24,7,1,
%e A187887 1275,492,201,84,31,8,1,
%t A187887 Select[Flatten[Table[Sum[Binomial[n-i,k]Binomial[2i,i],{i,0,n}],{n,0,10},{k,0,10}]],#!=0&] (* _Harvey P. Dale_, Jul 05 2012 *)
%o A187887 (Maxima) create_list(sum(binomial(n-i,k)*binomial(2*i,i), i,0,n),n,0,8,k,0,n);
%K A187887 nonn,easy,tabl
%O A187887 0,2
%A A187887 _Emanuele Munarini_, Mar 15 2011
%E A187887 Mathematica program corrected by _Harvey P. Dale_, Jul 05 2012
%E A187887 Comment added and comment corrected by _Michel Marcus_, Jun 23 2013