A210198 Triangle of coefficients of polynomials v(n,x) jointly generated with A210197; see the Formula section.

1, 3, 1, 7, 4, 15, 12, 1, 31, 32, 6, 63, 80, 24, 1, 127, 192, 80, 8, 255, 448, 240, 40, 1, 511, 1024, 672, 160, 10, 1023, 2304, 1792, 560, 60, 1, 2047, 5120, 4608, 1792, 280, 12, 4095, 11264, 11520, 5376, 1120, 84, 1, 8191, 24576, 28160, 15360, 4032

Offset

1,2

Comments

Row sums: A005409

Column 1: -1+2^n

Alternating row sums: 1, 2,3,4,5,6,..., A000027

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

Links

Table of n, a(n) for n=1..53.

Formula

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

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

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

Example

First five rows:
1
3....1
15...12...1
31...32...6
63...80...24...1
First three polynomials v(n,x): 1, 3 + x , 15 + 12x + x^2.

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := u[n - 1, x] + v[n - 1, x] + 1;
v[n_, x_] := (x + 1)*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[%]   (* A210197 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]  (* A210198 *)
Table[u[n, x] /. x -> 1, {n, 1, z}]  (* A048739 *)
Table[v[n, x] /. x -> 1, {n, 1, z}]  (* A005409 *)
Table[u[n, x] /. x -> -1, {n, 1, z}] (* A000217 *)
Table[v[n, x] /. x -> -1, {n, 1, z}] (* A000027 *)

Crossrefs

Cf. A210197, A208510.

Sequence in context: A269423 A328461 A341494 * A271258 A100584 A185877

Adjacent sequences: A210195 A210196 A210197 * A210199 A210200 A210201

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 18 2012

Status

approved