A208905 Triangle of coefficients of polynomials u(n,x) jointly generated with A208906; see the Formula section.

1, 1, 2, 1, 6, 2, 1, 12, 6, 4, 1, 20, 12, 20, 4, 1, 30, 20, 60, 20, 8, 1, 42, 30, 140, 60, 56, 8, 1, 56, 42, 280, 140, 224, 56, 16, 1, 72, 56, 504, 280, 672, 224, 144, 16, 1, 90, 72, 840, 504, 1680, 672, 720, 144, 32, 1, 110, 90, 1320, 840, 3696, 1680, 2640, 720

Offset

1,3

Comments

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

Links

Table of n, a(n) for n=1..64.

Formula

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

v(n,x)=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...6....2
1...12...6....4
1...20...12...20...4
First five polynomials u(n,x):
1
1 + 2x
1 + 6x + 2x^2
1 + 12x + 6x^2 + 4x^3
1 + 20x + 12x^2 + 20x^3 + 4x^4

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_] := 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[%]  (* A208905 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]  (* A208906 *)

Crossrefs

Cf. A208906, A208510.

Sequence in context: A248779 A286030 A343684 * A208749 A208751 A133200

Adjacent sequences: A208902 A208903 A208904 * A208906 A208907 A208908

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 03 2012

Status

approved