A208753 Triangle of coefficients of polynomials u(n,x) jointly generated with A208754; see the Formula section.

1, 1, 2, 1, 8, 1, 18, 4, 1, 32, 24, 1, 50, 80, 8, 1, 72, 200, 64, 1, 98, 420, 280, 16, 1, 128, 784, 896, 160, 1, 162, 1344, 2352, 864, 32, 1, 200, 2160, 5376, 3360, 384, 1, 242, 3300, 11088, 10560, 2464, 64, 1, 288, 4840, 21120, 28512, 11264, 896, 1

Offset

1,3

Comments

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

Links

Table of n, a(n) for n=1..56.

Formula

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

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

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

Example

First five rows:
1
1...2
1...8
1...18...4
1...32...24
First five polynomials u(n,x):
1
1 + 2x
1 + 8x
1 + 18x + 4x^2
1 + 32x + 24x^2

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := u[n - 1, x] + 2 x*v[n - 1, x];
v[n_, x_] := u[n - 1, 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[%]    (* A208753 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A208754 *)

Crossrefs

Cf. A208754, A208510.

Sequence in context: A009385 A008308 A176889 * A118931 A101280 A321280

Adjacent sequences: A208750 A208751 A208752 * A208754 A208755 A208756

Keyword

nonn,tabf

Author

Clark Kimberling, Mar 03 2012

Status

approved