%I A113214
%S A113214 1,2,1,0,3,1,0,2,4,1,0,0,5,5,1,0,0,2,9,6,1,0,0,0,7,14,7,1,0,0,0,2,16,20,
%T A113214 8,1,0,0,0,0,9,30,27,9,1,0,0,0,0,2,25,50,35,10,1,0,0,0,0,0,11,55,77,44,
%U A113214 11,1,0,0,0,0,0,2,36,105,112,54,12,1,0,0,0,0,0,0,13,91,182,156,65,13,1
%N A113214 Riordan array (1+2x,x(1+x)).
%C A113214 Row sums are Lucas numbers A000204. Diagonal sums are A007307(n+1). Inverse 
               is (-1)^(n-k)A092392(n,k). Product with Pascal triangle (1/(1-x),
               x/(1-x)) is A111125.
%F A113214 T(n, k)=C(k, n-k)+2C(k, n-k-1); T(n, k)=sum{j=0..n, (-1)^(n-j)*C(n, j)C(j+k, 
               2k)(2j+1)/(2k+1)}.
%e A113214 Triangle begins
%e A113214 1;
%e A113214 2,1;
%e A113214 0,3,1;
%e A113214 0,2,4,1;
%e A113214 0,0,5,5,1;
%e A113214 0,0,2,9,6,1;
%e A113214 0,0,0,7,14,7,1;
%e A113214 0,0,0,2,16,20,8,1;
%Y A113214 Sequence in context: A130055 A127013 A117362 this_sequence A029323 A071802 
               A110355
%Y A113214 Adjacent sequences: A113211 A113212 A113213 this_sequence A113215 A113216 
               A113217
%K A113214 easy,nonn,tabl
%O A113214 0,2
%A A113214 Paul Barry (pbarry(AT)wit.ie), Oct 18 2005