A209771 Triangle of coefficients of polynomials u(n,x) jointly generated with A209772; see the Formula section.

1, 1, 2, 2, 5, 4, 2, 9, 14, 8, 3, 14, 32, 36, 16, 3, 20, 60, 100, 88, 32, 4, 27, 100, 220, 288, 208, 64, 4, 35, 154, 420, 728, 784, 480, 128, 5, 44, 224, 728, 1568, 2240, 2048, 1088, 256, 5, 54, 312, 1176, 3024, 5376, 6528, 5184, 2432, 512, 6, 65, 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)=x*u(n-1,x)+(x+1)*v(n-1,x),

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

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

Example

First five rows:
1
1...2
2...5....4
2...9....14...8
3...14...32...36...16
First three polynomials u(n,x): 1, 1 + 2x, 2 + 5x + 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_] := (x + 1)*u[n - 1, x] + 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[%]    (* A209771 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A209772 *)

Crossrefs

Cf. A209772, A208510.

Sequence in context: A135281 A068465 A217876 * A209751 A275381 A283235

Adjacent sequences: A209768 A209769 A209770 * A209772 A209773 A209774

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 15 2012

Status

approved