A209752 Triangle of coefficients of polynomials v(n,x) jointly generated with A209751; see the Formula section.

1, 2, 2, 2, 6, 4, 3, 9, 16, 8, 3, 16, 33, 40, 16, 4, 20, 67, 105, 96, 32, 4, 30, 103, 242, 305, 224, 64, 5, 35, 169, 441, 793, 833, 512, 128, 5, 48, 230, 792, 1664, 2424, 2177, 1152, 256, 6, 54, 338, 1230, 3272, 5736, 7031, 5505, 2560, 512, 6, 70, 430

Offset

1,2

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

v(n,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
2...2
2...6....4
3...9....16...8
3...16...33...40...16
First three polynomials v(n,x): 1, 2 + 2x , 2 + 6x + 4x^2.

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := x*u[n - 1, x] + (x + 1)*v[n - 1, x];
v[n_, 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[%]    (* A209751 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A209752 *)

Crossrefs

Cf. A209651, A208510.

Sequence in context: A053695 A210550 A208659 * A119918 A084867 A194949

Adjacent sequences: A209749 A209750 A209751 * A209753 A209754 A209755

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 14 2012

Status

approved