OFFSET
1,2
COMMENTS
Column n is divisible by 2^(n-1); row n ends with 2^(n-1).
Column 2: 2*A004006.
FORMULA
u(n,x)=u(n-1,x)+v(n-1,x), v(n,x)=2x*u(n-1,x)+v(n-1,x)+1, where u(1,x)=1, v(1,x)=1.
EXAMPLE
First five rows:
1
2...2
3...6
4...14...4
5...28...20
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_] := 2 x*u[n - 1, x] + 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[%] (* A207622 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A207623 *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Feb 20 2012
STATUS
approved