A209556 Triangle of coefficients of polynomials v(n,x) jointly generated with A209555; see the Formula section.

1, 2, 1, 2, 3, 1, 3, 4, 4, 1, 3, 8, 7, 5, 1, 4, 9, 17, 11, 6, 1, 4, 15, 22, 31, 16, 7, 1, 5, 16, 43, 46, 51, 22, 8, 1, 5, 24, 50, 102, 86, 78, 29, 9, 1, 6, 25, 86, 130, 212, 148, 113, 37, 10, 1, 6, 35, 95, 250, 296, 400, 239, 157, 46, 11, 1, 7, 36, 150, 295, 626, 610

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..72.

Formula

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

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

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

Example

First five rows:
1
2...1
2...3...1
3...4...4...1
3...8...7...5...1
First three polynomials v(n,x): 1, 2 + 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_] := 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[%]    (* A209555 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A209556 *)

Crossrefs

Cf. A209555, A208510.

Sequence in context: A080786 A036838 A066010 * A109974 A213008 A215520

Adjacent sequences: A209553 A209554 A209555 * A209557 A209558 A209559

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 10 2012

Status

approved