OFFSET
1,5
COMMENTS
FORMULA
u(n,x)=u(n-1,x)+x*v(n-1,x),
v(n,x)=(x+2)*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
1...1
1...3...2
1...4...5....3
1...6...10...10...5
First three polynomials u(n,x): 1, 1 + x, 1 + 3x + 2x^2.
MATHEMATICA
u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := u[n - 1, x] + (x + j)*v[n - 1, x] + c;
d[x_] := h + x; e[x_] := p + x;
v[n_, x_] := d[x]*u[n - 1, x] + e[x]*v[n - 1, x] + f;
j = 0; c = 0; h = 2; p = -1; f = 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[%] (* A210797 *)
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A210798 *)
Table[u[n, x] /. x -> 1, {n, 1, z}] (* A099232 *)
Table[v[n, x] /. x -> 1, {n, 1, z}] (* A006130 *)
Table[u[n, x] /. x -> -1, {n, 1, z}] (* A008346 *)
Table[v[n, x] /. x -> -1, {n, 1, z}] (* A039834 *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Mar 26 2012
STATUS
approved