A209748 Triangle of coefficients of polynomials v(n,x) jointly generated with A209747; see the Formula section.

1, 3, 5, 2, 9, 6, 2, 15, 16, 8, 2, 25, 36, 26, 10, 2, 41, 76, 70, 38, 12, 2, 67, 152, 172, 118, 52, 14, 2, 109, 294, 394, 328, 182, 68, 16, 2, 177, 554, 860, 840, 562, 264, 86, 18, 2, 287, 1024, 1808, 2028, 1584, 894, 366, 106, 20, 2, 465, 1864, 3692, 4676

Offset

1,2

Comments

Alternating row sums: 1,3,3,5,5,7,7,9,9,...

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

Links

Table of n, a(n) for n=1..60.

Formula

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

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

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

Example

First five rows:
1
3
5....2
9....6....2
15...16...8...2
First three polynomials v(n,x): 1, 3, 5 + 2x.

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] + 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[%]    (* A209747 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A209748 *)

Crossrefs

Cf. A209647, A208510.

Sequence in context: A273668 A356472 A245653 * A065172 A026212 A026188

Adjacent sequences: A209745 A209746 A209747 * A209749 A209750 A209751

Keyword

nonn,tabf

Author

Clark Kimberling, Mar 13 2012

Status

approved