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

1, 2, 2, 3, 4, 2, 5, 9, 6, 2, 8, 18, 17, 8, 2, 13, 35, 41, 27, 10, 2, 21, 66, 93, 76, 39, 12, 2, 34, 122, 200, 196, 125, 53, 14, 2, 55, 222, 415, 472, 360, 190, 69, 16, 2, 89, 399, 837, 1083, 957, 603, 273, 87, 18, 2, 144, 710, 1651, 2392, 2400, 1750, 945, 376

Offset: 1

Author

Clark Kimberling, Feb 23 2012

Keywords

• nonn
• tabl

Comments

Column 1: Fibonacci numbers, A000045.

Examples

			First five rows:
1
2...2
3...4....2
5...9....6....2
8...18...17...8...2
		

Crossrefs

Cf. A207631.

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.