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

1, 1, 4, 1, 6, 10, 1, 8, 24, 28, 1, 10, 42, 88, 76, 1, 12, 64, 188, 300, 208, 1, 14, 90, 336, 760, 984, 568, 1, 16, 120, 540, 1560, 2880, 3136, 1552, 1, 18, 154, 808, 2820, 6672, 10416, 9792, 4240, 1, 20, 192, 1148, 4676, 13392, 26880, 36384, 30096

Offset

1,3

Comments

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
1...4
1...6...10
1...8...24...28
1...10...42...88...76
First three polynomials v(n,x): 1, 1 + 4x, 1 + 6x + 10x^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. A209160, A208510.

Sequence in context: A124739 A122662 A210228 * A338171 A333824 A083843

Adjacent sequences: A209158 A209159 A209160 * A209162 A209163 A209164

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 07 2012

Status

approved