A209751 Triangle of coefficients of polynomials u(n,x) jointly generated with A209752; see the Formula section.

1, 1, 2, 2, 5, 4, 2, 10, 15, 8, 3, 14, 35, 39, 16, 3, 22, 63, 108, 95, 32, 4, 27, 109, 235, 309, 223, 64, 4, 38, 160, 454, 782, 838, 511, 128, 5, 44, 242, 770, 1688, 2408, 2183, 1151, 256, 5, 58, 322, 1264, 3226, 5776, 7009, 5512, 2559, 512, 6, 65, 450

Offset

1,3

Comments

Alternating row sums: 1,-1,1,-1,1,-1,1,-1,...

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)=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...2
2...5....4
2...10...15...8
3...14...35...39...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_] := 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[%]    (* A209751 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A209752 *)

Crossrefs

Cf. A209752, A208510.

Sequence in context: A068465 A217876 A209771 * A275381 A283235 A209763

Adjacent sequences: A209748 A209749 A209750 * A209752 A209753 A209754

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 14 2012

Status

approved