A207631 Triangle of coefficients of polynomials u(n,x) jointly generated with A207632; see the Formula section.

1, 2, 4, 2, 7, 6, 2, 12, 15, 8, 2, 20, 33, 25, 10, 2, 33, 68, 66, 37, 12, 2, 54, 134, 159, 113, 51, 14, 2, 88, 256, 359, 309, 176, 67, 16, 2, 143, 478, 774, 781, 536, 257, 85, 18, 2, 232, 877, 1611, 1864, 1493, 860, 358, 105, 20, 2, 376, 1587, 3262, 4256

Offset: 1

Author

Clark Kimberling, Feb 23 2012

Keywords

• nonn
• tabf

Examples

			First five rows:
1
2
4...2
7...6...2
12...15...8...2
		

Crossrefs

Cf. A207632.

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_] := (x + 1)*u[n - 1, x] + x*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[%]  (* A207631 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]  (* A207632 *)

Formula

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

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

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