OFFSET
1,5
COMMENTS
Row sums = A083329: (1, 2, 5, 11, 23, 47, 95, ...).
From Clark Kimberling, Feb 28 2012: (Start)
FORMULA
Binomial transform of triangle A133566.
EXAMPLE
First few rows of the triangle:
1;
1, 1;
1, 3, 1;
1, 6, 3, 1;
1, 10, 6, 5, 1;
1, 15, 10, 15, 5, 1;
1, 21, 15, 35, 15, 7, 1;
...
MATHEMATICA
u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := u[n - 1, x] + x*v[n - 1, x];
v[n_, x_] := x*u[n - 1, x] + v[n - 1, x] + 1;
Table[Expand[u[n, x]], {n, 1, z/2}]
Table[Expand[v[n, x]], {n, 1, z/2}]
cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
TableForm[cu]
Flatten[%] (* A133567 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A133084 *)
(* Clark Kimberling, Feb 28 2012 *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Gary W. Adamson, Sep 16 2007
STATUS
approved