A187888 - OEIS

%I #8 Mar 30 2012 18:55:30

%S 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 7,1,3432,1275,492,201,84,31,8,1,12870,4707,1767,693,285,115,39,9,1,

%U 48620,17577,6474,2460,978,400,154,48,10,1,184756,66197,24051,8934,3438,1378,554,202,58,11,1

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

%F a(n,k) = [x^n] 1/sqrt(1-4*x)*(x/(1-x))^k.

%F 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 Recurrence: a(n+1,k+1) = a(n,k+1) + a(n,k)

%F G.f.: (1-x)/(sqrt(1-4*x)*(1-x-x*y)).

%e Triangle begins:

%e 1

%e 2,1

%e 6,3,1

%e 20,9,4,1

%e 70,29,13,5,1

%e 252,99,42,18,6,1

%e 924,351,141,60,24,7,1

%e 3432,1275,492,201,84,31,8,1

%o (Maxima) M(n,k):=pochhammer(n,k)/k!;

%o create_list(sum(M(k,n-k-i)*binomial(2*i,i),i,0,n-k),n,0,8,k,0,n);

%Y A187887

%K nonn,easy,tabl

%O 0,2

%A _Emanuele Munarini_, Mar 15 2011