login
A209566
Triangle of coefficients of polynomials v(n,x) jointly generated with A209565; see the Formula section.
3
1, 1, 3, 1, 3, 7, 1, 3, 10, 15, 1, 3, 10, 31, 31, 1, 3, 10, 34, 88, 63, 1, 3, 10, 34, 113, 233, 127, 1, 3, 10, 34, 116, 359, 586, 255, 1, 3, 10, 34, 116, 393, 1084, 1419, 511, 1, 3, 10, 34, 116, 396, 1306, 3120, 3340, 1023, 1, 3, 10, 34, 116, 396, 1349, 4216
OFFSET
1,3
COMMENTS
For a discussion and guide to related arrays, see A208510.
FORMULA
u(n,x)=x*u(n-1,x)+v(n-1,x),
v(n,x)=x*u(n-1,x)+2x*v(n-1,x) +1,
where u(1,x)=1, v(1,x)=1.
EXAMPLE
First five rows:
1
1...1
1...4...1
1...4...11...1
1...4...14...26...1
First three polynomials v(n,x): 1, 1 + x , 1 + 4x + x^2 .
MATHEMATICA
u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := x*u[n - 1, x] + v[n - 1, x];
v[n_, x_] := x*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[%] (* A209565 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A209566 *)
CROSSREFS
Sequence in context: A094250 A208517 A336203 * A208916 A209766 A356207
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Mar 10 2012
STATUS
approved