A208913 Triangle of coefficients of polynomials u(n,x) jointly generated with A208914; see the Formula section.

1, 1, 2, 1, 6, 4, 1, 12, 12, 8, 1, 20, 24, 40, 16, 1, 30, 40, 120, 80, 32, 1, 42, 60, 280, 240, 224, 64, 1, 56, 84, 560, 560, 896, 448, 128, 1, 72, 112, 1008, 1120, 2688, 1792, 1152, 256, 1, 90, 144, 1680, 2016, 6720, 5376, 5760, 2304, 512, 1, 110, 180

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)=2x*u(n-1,x)+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...12...8
1...20...24...40...16
First five polynomials u(n,x):
1
1 + 2x
1 + 6x + 4x^2
1 + 12x + 12x^2 + 8x^3
1 + 20x + 24x^2 + 40x^3 + 16x^4

Mathematica

u[n_, x_] := u[n - 1, x] + 2 x*v[n - 1, x];
v[n_, x_] := 2 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[%]    (* A208913 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A208914 *)

Crossrefs

Cf. A208914, A208510.

Sequence in context: A349573 A208923 A185045 * A208911 A208761 A123519

Adjacent sequences: A208910 A208911 A208912 * A208914 A208915 A208916

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 03 2012

Status

approved