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

Author

Clark Kimberling, Mar 13 2012

Keywords

• nonn
• tabf

Comments

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

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

Examples

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

Crossrefs

Cf. A209647, A208510.

Programs

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 *)

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.