0,2

Riordan array (c(x^2)/(1-2xc(x^2)),xc(x^2)) where c(x)=g.f. of Catalan numbers A000108 . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Mar 18 2007

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

Sum_{k, 0<=k<=n}T(n,k)=A127358(n) . T(n,0)=A054341(n).

Sum_{k, 0<=k<=n}T(n,k)*(-k+1)=2^n . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Mar 25 2007

Triangle begins:

1;

2, 1;

5, 2, 1;

12, 6, 2, 1;

30, 14, 7, 2, 1;

74, 37, 16, 8, 2, 1;

185, 90, 45, 18, 9, 2, 1;

460, 230, 108, 54, 20, 10, 2, 1;

1150, 568, 284, 128, 64, 22, 11, 2, 1;

2868, 1434, 696, 348, 150, 75, 24, 12, 2, 1;

Adjacent sequences: A126072 A126073 A126074 this_sequence A126076 A126077 A126078

Sequence in context: A105084 A126125 A128514 this_sequence A134032 A137151 A048494

nonn,tabl

Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Mar 02 2007