%I A124926
%S A124926 1,1,0,1,0,1,1,0,3,1,1,0,6,4,3,1,0,10,10,15,6,1,0,15,20,45,36,15,1,0,21,
%T A124926 35,105,126,105,36,1,0,28,56,210,336,420,288,91,1,0,36,84,378,756,1260,
%U A124926 1296,819,232,1,0,45,120,630,1512,3150,4320,4095,2320,603,1,0,55,165
%N A124926 Triangle read by rows: T(n,k)=binom(n,k)*r(k), where r(k) are the Riordan 
               numbers (r(k)=A005043(k); 0<=k<=n).
%C A124926 Row sums = Catalan numbers, A000108: (1, 1, 2, 5, 14, 42...); e.g. sum 
               of row 4 terms = A000108(4) = 14 = (1 + 0 + 6 + 4 + 3). A005043 is 
               the inverse binomial transform of the Catalan numbers.
%e A124926 First few rows of the triangle are:
%e A124926 1;
%e A124926 1, 0;
%e A124926 1, 0, 1;
%e A124926 1, 0, 3, 1;
%e A124926 1, 0, 6, 4, 3;
%e A124926 1, 0, 10, 10, 15, 6;
%e A124926 1, 0, 15, 20, 45, 36, 15;
%e A124926 ...
%p A124926 r:=n->(1/(n+1))*sum((-1)^i*binomial(n+1,i)*binomial(2*n-2*i,n-i),i=0..n): 
               T:=(n,k)->r(k)*binomial(n,k): for n from 0 to 11 do seq(T(n,k),k=0..n) 
               od; # yields sequence in triangular form
%Y A124926 Cf. A005043, A000108.
%Y A124926 Sequence in context: A130160 A162169 A124801 this_sequence A115378 A120060 
               A143295
%Y A124926 Adjacent sequences: A124923 A124924 A124925 this_sequence A124927 A124928 
               A124929
%K A124926 nonn,tabl
%O A124926 0,9
%A A124926 Gary W. Adamson (qntmpkt(AT)yahoo.com), Nov 12 2006
%E A124926 Edited by N. J. A. Sloane (njas(AT)research.att.com), Nov 29 2006