A210225 Triangle of coefficients of polynomials u(n,x) jointly generated with A210226; see the Formula section.

1, 2, 1, 3, 5, 1, 4, 12, 10, 1, 5, 22, 36, 17, 1, 6, 35, 88, 87, 26, 1, 7, 51, 175, 277, 181, 37, 1, 8, 70, 306, 680, 734, 338, 50, 1, 9, 92, 490, 1416, 2196, 1710, 582, 65, 1, 10, 117, 736, 2632, 5402, 6156, 3606, 941, 82, 1, 11, 145, 1053, 4502, 11592

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...5....1
4...12...10...1
5...22...36...17...1
First three polynomials u(n,x): 1, 2 + x, 3 + 5x + x^2.
		

Crossrefs

Cf. A210226, 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_] := 2 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[%]     (* A210225 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]     (* A210226 *)

Formula

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

v(n,x)=2x*u(n-1,x)+(x+1)*v(n-1,x)+1,

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