A208911 Triangle of coefficients of polynomials u(n,x) jointly generated with A208912; see the Formula section.

1, 1, 2, 1, 6, 4, 1, 12, 14, 8, 1, 20, 32, 38, 16, 1, 30, 60, 110, 90, 32, 1, 42, 100, 250, 300, 214, 64, 1, 56, 154, 490, 770, 826, 490, 128, 1, 72, 224, 868, 1680, 2408, 2128, 1110, 256, 1, 90, 312, 1428, 3276, 5880, 6888, 5382, 2474, 512, 1, 110, 420

Offset

1,3

Comments

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

Links

Table of n, a(n) for n=1..58.

Formula

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

v(n,x)=x*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...2
1...6....4
1...12...14...8
1...20...32...38...16
First five polynomials u(n,x):
1
1 + 2x
1 + 6x + 4x^2
1 + 12x + 14x^2 + 8x^3
1 + 20x + 32x^2 + 38x^3 + 16x^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] + (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[%]    (* A208911 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A208912 *)

Crossrefs

Cf. A208912, A208510.

Sequence in context: A208923 A185045 A208913 * A208761 A123519 A167024

Adjacent sequences: A208908 A208909 A208910 * A208912 A208913 A208914

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 03 2012

Status

approved