A207620 Triangle of coefficients of polynomials u(n,x) jointly generated with A207621; see the Formula section.

1, 2, 4, 2, 7, 8, 2, 11, 21, 12, 2, 16, 45, 43, 16, 2, 22, 85, 119, 73, 20, 2, 29, 147, 280, 249, 111, 24, 2, 37, 238, 588, 705, 451, 157, 28, 2, 46, 366, 1134, 1749, 1496, 741, 211, 32, 2, 56, 540, 2046, 3927, 4290, 2821, 1135, 273, 36, 2, 67, 770, 3498

Offset: 1

Author

Clark Kimberling, Feb 20 2012

Keywords

• nonn
• tabf

Examples

			First five rows:
1
2
4...2
7...8...2
11...21...12...2
		

Crossrefs

Cf. A207621.

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*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[%]    (* A207620 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A207621 *)

Formula

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

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

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