OFFSET
1,2
COMMENTS
Riordan array ((1 + z)/(1 - 2*z), z*(1 - z)/(1 - 2*z)). - Peter Bala, Dec 31 2015
FORMULA
u(n,x) = u(n-1,x) + v(n-1,x),
v(n,x) = u(n-1,x) + (x + 1)*v(n-1,x) + 1,
where u(1,x) = 1, v(1,x) = 1.
EXAMPLE
First five rows:
1
3 1
6 4 1
12 11 5 1
24 28 17 6 1
MATHEMATICA
u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := u[n - 1, x] + v[n - 1, x]
v[n_, x_] := u[n - 1, x] + (x + 1)*v[n - 1, x] + 1
Table[Factor[u[n, x]], {n, 1, z}]
Table[Factor[v[n, x]], {n, 1, z}]
cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
TableForm[cu]
Flatten[%] (* A207614 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A207615 *)
CROSSREFS
KEYWORD
AUTHOR
Clark Kimberling, Feb 20 2012
STATUS
approved