A209754 Triangle of coefficients of polynomials v(n,x) jointly generated with A209753; see the Formula section.

1, 3, 1, 5, 6, 1, 9, 16, 10, 1, 15, 39, 38, 15, 1, 25, 84, 117, 76, 21, 1, 41, 172, 308, 286, 136, 28, 1, 67, 337, 744, 894, 612, 225, 36, 1, 109, 642, 1685, 2496, 2228, 1191, 351, 45, 1, 177, 1196, 3646, 6423, 7088, 4978, 2157, 523, 55, 1, 287, 2191

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..57.

Formula

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

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

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

Example

First five rows:
1
3....1
5....6....1
9....16...10...1
15...39...38...15...1
First three polynomials v(n,x): 1, 3 + x , 5 + 6x + x^2.

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := x*u[n - 1, x] + (x + 1)*v[n - 1, x];
v[n_, x_] := u[n - 1, x] + (x + 1)*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[%]    (* A209753 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A209754 *)

Crossrefs

Cf. A209653, A208510.

Sequence in context: A108283 A208904 A344479 * A140950 A256504 A205713

Adjacent sequences: A209751 A209752 A209753 * A209755 A209756 A209757

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 14 2012

Status

approved