OFFSET
1,2
COMMENTS
FORMULA
u(n,x)=(x+1)*u(n-1,x)+v(n-1,x)+1,
v(n,x)=(x+1)*u(n-1,x)+2x*v(n-1,x)+1,
where u(1,x)=1, v(1,x)=1.
EXAMPLE
First five rows:
1
2....3
4....8....7
7....21...24...15
12...46...78...64...31
First three polynomials v(n,x): 1, 2 + 3x, 4 + 8x +7x^2
MATHEMATICA
u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := (x + 1)*u[n - 1, x] + v[n - 1, x] + 1;
v[n_, x_] := (x + 1)*u[n - 1, x] + 2 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[%] (* A210749 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A210750 *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Mar 25 2012
STATUS
approved