%I A050165
%S A050165 1,1,1,1,3,2,1,5,9,5,1,7,20,28,14,1,9,35,75,90,42,1,11,54,154,275,297,
%T A050165 132,1,13,77,273,637,1001,1001,429,1,15,104,440,1260,2548,3640,3432,
%U A050165 1430,1,17,135,663,2244,5508,9996,13260,11934
%N A050165 T(n,k)=M(2n+1,k,-1), 0<=k<=n, n >= 0, array M as in A050144.
%C A050165 T is a mirror image of the array in A039599.
%F A050165 Triangle T(n, k) read by rows; given by [1, 0, 0, 0, 0, 0, 0, 0, ...] 
               DELTA [1, 1, 1, 1, 1, 1, 1, 1, 1, ...] where DELTA is the operator 
               defined in A084938. T(n, k) = C(2n, k)*(2n-2k+1)/(2n-k+1) . - DELEHAM 
               Philippe (kolotoko(AT)wanadoo.fr), Dec 07 2003
%F A050165 Sum_{k=0 ..inf(m, n)} T(m, m-k)*T(n, n-k)= A000108(m+n); A000108: Catalan 
               numbers. - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Dec 30 2003
%F A050165 T(n, k) = 0 if n<k, T(n, n)= A000108(n) and for n>k : T(n, k) = Sum_{j=0..k} 
               T(n-1-j, k-j)*A000108(j+1) . - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), 
               Feb 03 2004
%F A050165 T(n,k)= Sum_{j, j>=0} (-1)^(n-j)*A094385(n,j)*binomial(j,k) . - Philippe 
               DELEHAM (kolotoko(AT)wanadoo.fr), May 05 2007
%e A050165 Rows: {1}; {1,1}; {1,3,2}; ...
%Y A050165 Cf. A084938.
%Y A050165 Sequence in context: A077976 A021912 A114597 this_sequence A033878 A144061 
               A085792
%Y A050165 Adjacent sequences: A050162 A050163 A050164 this_sequence A050166 A050167 
               A050168
%K A050165 nonn,tabl
%O A050165 0,5
%A A050165 Clark Kimberling (ck6(AT)evansville.edu)