A207626 Triangle of coefficients of polynomials v(n,x) jointly generated with A207625; see the Formula section.

1, 2, 3, 3, 9, 3, 4, 20, 18, 3, 5, 38, 62, 27, 3, 6, 65, 164, 131, 36, 3, 7, 103, 369, 461, 227, 45, 3, 8, 154, 742, 1324, 1010, 350, 54, 3, 9, 220, 1372, 3298, 3578, 1892, 500, 63, 3, 10, 303, 2376, 7386, 10768, 8022, 3188, 677, 72, 3, 11, 405, 3903, 15222

Offset: 1

Author

Clark Kimberling, Feb 21 2012

Keywords

• nonn
• tabl

Examples

			First five rows:
1
2...3
3...9...3
4...20...18...3
5...38...62...27...3
		

Crossrefs

Cf. A207625.

Programs

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := u[n - 1, x] + v[n - 1, x]
v[n_, x_] := 2 x*u[n - 1, x] + (x + 1)*v[n - 1, x] + 1
Table[Factor[u[n, x]], {n, 1, z}]
Table[Factor[v[n, x]], {n, 1, z}]
cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
TableForm[cu]
Flatten[%]    (* A207625 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A207626 *)

Formula

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

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

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