A207633 Triangle of coefficients of polynomials u(n,x) jointly generated with A207634; see the Formula section.

1, 2, 4, 3, 7, 9, 6, 12, 22, 21, 12, 20, 48, 62, 48, 24, 33, 98, 157, 163, 108, 48, 54, 192, 367, 463, 410, 240, 96, 88, 365, 810, 1203, 1281, 1000, 528, 192, 143, 679, 1715, 2919, 3634, 3392, 2384, 1152, 384, 232, 1242, 3518, 6742, 9550, 10379, 8696

Offset: 1

Author

Clark Kimberling, Feb 24 2012

Keywords

• nonn
• tabf

Examples

			First five rows:
1
2
4....3
7....9....6
12...22...21...12
		

Crossrefs

Cf. A207634.

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] + 2 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[%]  (* A207633 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]  (* A207634 *)

Formula

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

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

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