A208521 Triangle of coefficients of polynomials v(n,x) jointly generated with A208520; see the Formula section.

1, 2, 2, 3, 4, 2, 4, 6, 8, 4, 5, 8, 20, 16, 4, 6, 10, 40, 40, 24, 8, 7, 12, 70, 80, 84, 48, 8, 8, 14, 112, 140, 224, 168, 64, 16, 9, 16, 168, 224, 504, 448, 288, 128, 16, 10, 18, 240, 336, 1008, 1008, 960, 576, 160, 32, 11, 20, 330, 480, 1848, 2016, 2640, 1920

Offset

1,2

Links

Table of n, a(n) for n=1..63.

Formula

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

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

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

Example

First five rows:
1
2...2
3...4...2
4...6...8....4
5...8...20...16...4
First five polynomials v(n,x):
1
2 + 2x
3 + 4x + 2x^2
4 + 6x + 8x^2 + 4x^3
5 + 8x + 20x^2 + 16x^3 + 4x^4

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := u[n - 1, x] + x*v[n - 1, x];
v[n_, x_] := 2 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[%]    (* A208520 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A208521 *)

Crossrefs

Cf. A208520.

Sequence in context: A290600 A143595 A211702 * A209570 A205703 A363100

Adjacent sequences: A208518 A208519 A208520 * A208522 A208523 A208524

Keyword

nonn,tabl

Author

Clark Kimberling, Feb 28 2012

Status

approved