A209579 Triangle of coefficients of polynomials u(n,x) jointly generated with A209580; see the Formula section.

1, 1, 1, 2, 3, 1, 2, 6, 6, 1, 3, 9, 14, 10, 1, 3, 14, 28, 29, 15, 1, 4, 18, 48, 71, 55, 21, 1, 4, 25, 75, 139, 158, 97, 28, 1, 5, 30, 112, 251, 356, 321, 161, 36, 1, 5, 39, 156, 413, 724, 828, 609, 254, 45, 1, 6, 45, 215, 645, 1321, 1874, 1782, 1094, 384, 55, 1, 6

Offset

1,4

Comments

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

Links

Table of n, a(n) for n=1..67.

Formula

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

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

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

Example

First five rows:
1
1...1
2...3....1
2...6....6....1
3...9....14...10...1
First three polynomials v(n,x): 1, 1 + x, 2 + 3x + 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] + 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[%]   (* A209579 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]   (* A209580 *)

Crossrefs

Cf. A209580, A208510.

Sequence in context: A154948 A109091 A138507 * A205699 A109200 A158909

Adjacent sequences: A209576 A209577 A209578 * A209580 A209581 A209582

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 11 2012

Status

approved