A209575 Triangle of coefficients of polynomials u(n,x) jointly generated with A209576; see the Formula section.

1, 1, 1, 1, 5, 1, 1, 5, 15, 1, 1, 5, 23, 37, 1, 1, 5, 23, 89, 83, 1, 1, 5, 23, 105, 295, 177, 1, 1, 5, 23, 105, 447, 873, 367, 1, 1, 5, 23, 105, 479, 1721, 2383, 749, 1, 1, 5, 23, 105, 479, 2121, 6015, 6137, 1515, 1, 1, 5, 23, 105, 479, 2185, 8847, 19369, 15143

Offset

1,5

Comments

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

Links

Table of n, a(n) for n=1..64.

Formula

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

v(n,x)=2x*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...5...1
1...5...15...1
1...5...23...37...1
First three polynomials v(n,x): 1, 1 + x, 1 + 5x + 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_] := 2 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[%]   (* A209575 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]   (* A209576 *)

Crossrefs

Cf. A209576, A208510.

Sequence in context: A071856 A242133 A144221 * A159570 A280374 A259975

Adjacent sequences: A209572 A209573 A209574 * A209576 A209577 A209578

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 11 2012

Status

approved