A209565 Triangle of coefficients of polynomials u(n,x) jointly generated with A209566; see the Formula section.

1, 1, 1, 1, 4, 1, 1, 4, 11, 1, 1, 4, 14, 26, 1, 1, 4, 14, 45, 57, 1, 1, 4, 14, 48, 133, 120, 1, 1, 4, 14, 48, 161, 366, 247, 1, 1, 4, 14, 48, 164, 520, 952, 502, 1, 1, 4, 14, 48, 164, 557, 1604, 2371, 1013, 1, 1, 4, 14, 48, 164, 560, 1863, 4724, 5711, 2036, 1, 1, 4

Offset

1,5

Comments

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

Links

Table of n, a(n) for n=1..68.

Formula

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

v(n,x)=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
1...1
1...4....1
1...4....11...1
1...4...14...26...1
First three polynomials v(n,x): 1, 1 + x, 1 + 4x + x^2.

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := x*u[n - 1, x] + v[n - 1, x];
v[n_, x_] := 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[%]   (* A209565 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]   (* A209566 *)

Crossrefs

Cf. A209566, A208510.

Sequence in context: A124258 A001638 A133826 * A122185 A350000 A193752

Adjacent sequences: A209562 A209563 A209564 * A209566 A209567 A209568

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 10 2012

Status

approved