A209578 Triangle of coefficients of polynomials v(n,x) jointly generated with A209577; see the Formula section.

1, 3, 1, 5, 3, 1, 9, 8, 4, 1, 15, 19, 13, 5, 1, 25, 41, 36, 19, 6, 1, 41, 84, 90, 60, 26, 7, 1, 67, 165, 210, 169, 92, 34, 8, 1, 109, 315, 465, 439, 287, 133, 43, 9, 1, 177, 588, 990, 1073, 818, 454, 184, 53, 10, 1, 287, 1079, 2043, 2502, 2178, 1405, 681, 246

Offset

1,2

Comments

Alternating row sums: 1,0,2,1,3,2,4,3,5,4,... (A028242).

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

Links

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

Formula

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

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
1...1
3...2....1
5...6....3....1
9...13...10...4...1
First three polynomials v(n,x): 1, 1 + x , 3 + 2x + x^2.

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := x*u[n - 1, x] + v[n - 1, x];
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[%]   (* A209577 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]   (* A209578 *)

Crossrefs

Cf. A209577, A208510.

Sequence in context: A060439 A206283 A135224 * A268829 A249100 A356255

Adjacent sequences: A209575 A209576 A209577 * A209579 A209580 A209581

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 11 2012

Status

approved