A209560 Triangle of coefficients of polynomials v(n,x) jointly generated with A209559; see the Formula section.

1, 3, 1, 5, 5, 1, 9, 12, 7, 1, 15, 29, 22, 9, 1, 25, 61, 66, 35, 11, 1, 41, 124, 166, 125, 51, 13, 1, 67, 241, 394, 365, 211, 70, 15, 1, 109, 457, 877, 988, 701, 329, 92, 17, 1, 177, 848, 1877, 2472, 2129, 1225, 484, 117, 19, 1, 287, 1549, 3884, 5880, 5909

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..60.

Formula

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

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

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

Example

First five rows:
1
3....1
5....5....1
9....12...7....1
15...29...22...9...1
First three polynomials v(n,x): 1, 3 + x , 5 + 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_] := u[n - 1, x] + (x + 1)*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[%]   (* A209559 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]   (* A209560 *)

Crossrefs

Cf. A209559, A208510.

Sequence in context: A182397 A343510 A344725 * A211977 A072919 A273171

Adjacent sequences: A209557 A209558 A209559 * A209561 A209562 A209563

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 10 2012

Status

approved