A210231 Triangle of coefficients of polynomials u(n,x) jointly generated with A210232; see the Formula section.

1, 2, 1, 3, 4, 1, 4, 8, 7, 1, 5, 14, 18, 11, 1, 6, 21, 39, 36, 16, 1, 7, 30, 69, 93, 66, 22, 1, 8, 40, 114, 192, 199, 113, 29, 1, 9, 52, 172, 360, 474, 393, 183, 37, 1, 10, 65, 250, 610, 997, 1068, 729, 283, 46, 1, 11, 80, 345, 980, 1882, 2501, 2238, 1285, 421

Offset: 1

Author

Clark Kimberling, Mar 20 2012

Keywords

• nonn
• tabl

Comments

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

Examples

			First five rows:
1
2...1
3...4....1
4...8....7....1
5...14...18...11...1
First three polynomials u(n,x): 1, 2 + x, 3 + 4x + x^2.
		

Crossrefs

Cf. A210232, A208510.

Programs

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := x*u[n - 1, x] + v[n - 1, x] + 1;
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[%]     (* A210231 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]     (* A210232 *)

Formula

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

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

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