A187887 Riordan matrix (1/((1-x)*sqrt(1-4*x)),x/(1-x)).
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, 31, 8, 1, 4707, 1767, 693, 285, 115, 39, 9, 1, 17577, 6474, 2460, 978, 400, 154, 48, 10, 1, 66197, 24051, 8934, 3438, 1378, 554, 202, 58, 11, 1, 250953, 90248, 32985, 12372, 4816, 1932, 756, 260, 69, 12, 1
Offset: 0
Examples
Triangle begins: 1, 3,1, 9,4,1, 29,13,5,1, 99,42,18,6,1, 351,141,60,24,7,1, 1275,492,201,84,31,8,1,
Programs
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Mathematica
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 *) -
Maxima
create_list(sum(binomial(n-i,k)*binomial(2*i,i), i,0,n),n,0,8,k,0,n);
Formula
a(n,k) = [x^n] 1/((1-x)*sqrt(1-4*x))*(x/(1-x))^k.
Recurrence: a(n+1,k+1) = a(n,k+1) + a(n,k).
a(n,k) = sum(binomial(n-i,k)*binomial(2*i,i),i=0..n).
G.f.: 1/(sqrt(1-4*x)*(1-x-x*y)).
Extensions
Mathematica program corrected by Harvey P. Dale, Jul 05 2012
Comment added and comment corrected by Michel Marcus, Jun 23 2013
Comments