A210556 Triangle of coefficients of polynomials v(n,x) jointly generated with A210555; see the Formula section.

1, 2, 2, 3, 4, 4, 4, 6, 10, 8, 5, 8, 18, 22, 16, 6, 10, 28, 42, 50, 32, 7, 12, 40, 68, 106, 110, 64, 8, 14, 54, 100, 188, 250, 242, 128, 9, 16, 70, 138, 300, 468, 594, 526, 256, 10, 18, 88, 182, 446, 780, 1188, 1378, 1138, 512, 11, 20, 108, 232, 630, 1202

Offset: 1

Author

Clark Kimberling, Mar 22 2012

Keywords

• nonn
• tabl

Comments

Alternating row sums: 1,0,3,0,9,0,27,0,81,0,...

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

Examples

			First five rows:
1
2...2
3...4...4
4...6...10...8
5...8...18...22...16
First three polynomials v(n,x): 1, 2 + 2x , 3 + 4x + 4x^2.
		

Crossrefs

Cf. A210555, A208510.

Programs

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := x*u[n - 1, x] + x*v[n - 1, x] + 1;
v[n_, x_] := 2 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[%]   (* A210555 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]   (* A210556 *)

Formula

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

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

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