A209558 Triangle of coefficients of polynomials v(n,x) jointly generated with A209557; see the Formula section.

1, 2, 2, 2, 5, 4, 3, 7, 11, 8, 3, 13, 21, 23, 16, 4, 15, 44, 57, 47, 32, 4, 24, 60, 129, 145, 95, 64, 5, 26, 108, 207, 346, 353, 191, 128, 5, 38, 130, 405, 646, 875, 833, 383, 256, 6, 40, 212, 545, 1345, 1877, 2124, 1921, 767, 512, 6, 55, 240, 965, 2021

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)+2x*v(n-1,x)+1,

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

Example

First five rows:
1
2...2
2...5...4
3...7...11...8
3...13...21...23...16
First three polynomials v(n,x): 1, 2 + 2x , 2+ 5x + 4x^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] + 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[%]    (* A209557 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A209558 *)

Crossrefs

Cf. A209557, A208510.

Sequence in context: A210562 A208512 A208908 * A209772 A370164 A147293

Adjacent sequences: A209555 A209556 A209557 * A209559 A209560 A209561

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 10 2012

Status

approved