A209701 Triangle of coefficients of polynomials u(n,x) jointly generated with A209702; see the Formula section.

1, 0, 2, 0, 2, 5, 0, 3, 7, 12, 0, 4, 11, 23, 29, 0, 5, 16, 41, 70, 70, 0, 6, 22, 66, 140, 204, 169, 0, 7, 29, 99, 247, 455, 577, 408, 0, 8, 37, 141, 401, 875, 1423, 1597, 985, 0, 9, 46, 193, 613, 1529, 2965, 4321, 4348, 2378, 0, 10, 56, 256, 895, 2495, 5549

Offset

1,3

Comments

For a discussion and guide to related arrays, see A208510.

Links

Table of n, a(n) for n=1..62.

Formula

u(n,x)=x*u(n-1,x)+x*v(n-1,x),

v(n,x)=2x*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
0...2
0...2...5
0...3...7....12
0...4...11...23...29
First three polynomials v(n,x): 1, 2x, 2x + 5x^2.

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := x*u[n - 1, x] + x*v[n - 1, x];
v[n_, x_] := 2 x*u[n - 1, x] + (x + 1)*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[%]  (* A209701 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]  (* A209702 *)

Crossrefs

Cf. A209702, A208510.

Sequence in context: A052438 A324045 A358405 * A158855 A344908 A005074

Adjacent sequences: A209698 A209699 A209700 * A209702 A209703 A209704

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 12 2012

Status

approved