A209160 Triangle of coefficients of polynomials u(n,x) jointly generated with A209161; see the Formula section.

1, 2, 1, 3, 6, 4, 4, 13, 20, 10, 5, 22, 52, 62, 28, 6, 33, 104, 192, 192, 76, 7, 46, 180, 444, 680, 584, 208, 8, 61, 284, 870, 1776, 2328, 1760, 568, 9, 78, 420, 1530, 3876, 6768, 7776, 5256, 1552, 10, 97, 592, 2492, 7504, 16260, 24864, 25464, 15584

Offset

1,2

Comments

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

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

Links

Table of n, a(n) for n=1..54.

Formula

u(n,x)=u(n-1,x)+(x+1)*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
2...1
3...6....4
4...13...20...10
5...22...52...62...28
First three polynomials v(n,x): 1, 2 + x, 3 + 6x + 4x^2.

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := u[n - 1, x] + (x + 1)*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[%]    (* A209160 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A209161 *)

Crossrefs

Cf. A209161, A208510.

Sequence in context: A347297 A133904 A245182 * A371418 A340406 A257881

Adjacent sequences: A209157 A209158 A209159 * A209161 A209162 A209163

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 07 2012

Status

approved