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

1, 2, 4, 3, 7, 12, 3, 11, 32, 21, 3, 16, 70, 83, 30, 3, 22, 135, 247, 161, 39, 3, 29, 238, 616, 622, 266, 48, 3, 37, 392, 1358, 1946, 1276, 398, 57, 3, 46, 612, 2730, 5244, 4854, 2290, 557, 66, 3, 56, 915, 5106, 12630, 15622, 10312, 3745, 743, 75, 3, 67

Offset: 1

Author

Clark Kimberling, Feb 21 2012

Keywords

• nonn
• tabf

Examples

			First five rows:
1
2
4....3
7....12...3
11...32...21...3
		

Crossrefs

Cf. A207626.

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.