%I A126791
%S A126791 1,4,1,17,7,1,75,39,10,1,339,202,70,13,1,1558,1015,425,110,16,1,7247,
%T A126791 5028,2400,771,159,19,1,34016,24731,12999,4872,1267,217,22,1,160795,
%U A126791 121208,68600,28882,8890,1940,284,25,1,764388,593019,354890,164136
%N A126791 Binomial matrix applied to A111418.
%C A126791 Triangle T(n,k), 0<=k<=n, read by rows defined by : T(0,0)=1, T(n,k)=0 
               if k<0 or if k>n, T(n,0)=4*T(n-1,0)+T(n-1,1), T(n,k)=T(n-1,k-1)+3*T(n-1,
               k)+T(n-1,k+1) for k>=1.
%C A126791 This triangle belongs to the family of triangles defined by: T(0,0)=1, 
               T(n,k)=0 if k<0 or if k>n, T(n,0)=x*T(n-1,0)+T(n-1,1), T(n,k)=T(n-1,
               k-1)+y*T(n-1,k)+T(n-1,k+1) for k>=1 . Other triangles arise by choosing 
               different values for (x,y): (0,0) -> A053121; (0,1) -> A089942; (0,
               2) -> A126093; (0,3) -> A126970; (1,0)-> A061554; (1,1) -> A064189; 
               (1,2) -> A039599; (1,3) -> A110877; ((1,4) -> A124576; (2,0) -> A126075; 
               (2,1) -> A038622; (2,2) -> A039598; (2,3) -> A124733; (2,4) -> A124575; 
               (3,0) -> A126953; (3,1) -> A126954; (3,2) -> A111418; (3,3) -> A091965; 
               (3,4) -> A124574; (4,3) -> A126791; (4,4) -> A052179; (4,5) -> A126331; 
               (5,5) -> A125906 . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Sep 
               25 2007
%F A126791 Sum{k, k>=0}T(m,k)*T(n,k)=T(m+n,0)=A026378(m+n+1) . Sum{k, 0<=k<=n}T(n,
               k)=5^n=A000351(n).
%e A126791 Triangle begins:
%e A126791 1;
%e A126791 4, 1;
%e A126791 17, 7, 1;
%e A126791 75, 39, 10, 1;
%e A126791 339, 202, 70, 13, 1;
%e A126791 1558, 1015, 425, 110, 16, 1;
%e A126791 7247, 5028, 2400, 771, 159, 19, 1;
%e A126791 34016, 24731, 12999, 4872, 1267, 217, 22, 1;...
%Y A126791 Sequence in context: A111661 A072651 A093035 this_sequence A052179 A126331 
               A013631
%Y A126791 Adjacent sequences: A126788 A126789 A126790 this_sequence A126792 A126793 
               A126794
%K A126791 nonn,tabl
%O A126791 0,2
%A A126791 Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Mar 14 2007