A208906 Triangle of coefficients of polynomials v(n,x) jointly generated with A208905; see the Formula section.

1, 2, 1, 3, 2, 2, 4, 3, 8, 2, 5, 4, 20, 8, 4, 6, 5, 40, 20, 24, 4, 7, 6, 70, 40, 84, 24, 8, 8, 7, 112, 70, 224, 84, 64, 8, 9, 8, 168, 112, 504, 224, 288, 64, 16, 10, 9, 240, 168, 1008, 504, 960, 288, 160, 16, 11, 10, 330, 240, 1848, 1008, 2640, 960, 880, 160, 32

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..66.

Formula

u(n,x)=u(n-1,x)+2x*v(n-1,x),

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

where u(1,x)=1, v(1,x)=1.

Example

First five rows:
1
2...1
3...2...2
4...3...8....2
5...4...20...8...4
First five polynomials v(n,x):
1
2 + x
3 + 2x + 2x^2
4 + 3x + 8x^2 + 2x^3
5 + 4x + 20x^2 + 8x^3 + 4x^4

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := u[n - 1, x] + 2 x*v[n - 1, x];
v[n_, x_] := x*u[n - 1, 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[%]    (* A208905 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A208906 *)

Crossrefs

Cf. A208905, A208510.

Sequence in context: A137948 A210553 A269456 * A120933 A209756 A210795

Adjacent sequences: A208903 A208904 A208905 * A208907 A208908 A208909

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 03 2012

Status

approved