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A187888 Riordan matrix (1/sqrt(1-4*x),x/(1-x)).

%I A187888 #8 Mar 30 2012 18:55:30
%S A187888 1,2,1,6,3,1,20,9,4,1,70,29,13,5,1,252,99,42,18,6,1,924,351,141,60,24,
%T A187888 7,1,3432,1275,492,201,84,31,8,1,12870,4707,1767,693,285,115,39,9,1,
%U A187888 48620,17577,6474,2460,978,400,154,48,10,1,184756,66197,24051,8934,3438,1378,554,202,58,11,1
%N A187888 Riordan matrix (1/sqrt(1-4*x),x/(1-x)).
%F A187888 a(n,k) = [x^n] 1/sqrt(1-4*x)*(x/(1-x))^k.
%F A187888 a(n,k) = sum(M(k,n-k-i)*binomial(2*i,i),i=0..n-k) where M(n,k) = n*(n+1)*(n+2)...(n+k-1)/k!.
%F A187888 Recurrence: a(n+1,k+1) = a(n,k+1) + a(n,k)
%F A187888 G.f.: (1-x)/(sqrt(1-4*x)*(1-x-x*y)).
%e A187888 Triangle begins:
%e A187888 1
%e A187888 2,1
%e A187888 6,3,1
%e A187888 20,9,4,1
%e A187888 70,29,13,5,1
%e A187888 252,99,42,18,6,1
%e A187888 924,351,141,60,24,7,1
%e A187888 3432,1275,492,201,84,31,8,1
%o A187888 (Maxima) M(n,k):=pochhammer(n,k)/k!;
%o A187888 create_list(sum(M(k,n-k-i)*binomial(2*i,i),i,0,n-k),n,0,8,k,0,n);
%Y A187888 A187887
%K A187888 nonn,easy,tabl
%O A187888 0,2
%A A187888 _Emanuele Munarini_, Mar 15 2011