A208527 Triangle of coefficients of polynomials v(n,x) jointly generated with A208526; see the Formula section.

1, 1, 4, 1, 4, 10, 1, 4, 12, 28, 1, 4, 14, 40, 76, 1, 4, 16, 52, 124, 208, 1, 4, 18, 64, 176, 384, 568, 1, 4, 20, 76, 232, 592, 1168, 1552, 1, 4, 22, 88, 292, 832, 1936, 3520, 4240, 1, 4, 24, 100, 356, 1104, 2880, 6240, 10512, 11584, 1, 4, 26, 112, 424, 1408

Offset: 1

Author

Clark Kimberling, Feb 29 2012

Keywords

• nonn
• tabl

Examples

			First five rows:
1
1...4
1...4...10
1...4...12...28
1...4...14...40...76
First five polynomials v(n,x):
1
1 + 4x
1 + 4x + 10x^2
1 + 4x + 12x^2 + 28x^3
1 + 4x + 14x^2 + 40x^3 + 76x^4
		

Crossrefs

Cf. A208526.

Programs

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := u[n - 1, x] + x*v[n - 1, x];
v[n_, x_] := 2 x*u[n - 1, x] + 2 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[%]  (* A208526 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]  (* A208527 *)

Formula

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

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

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