A207623 Triangle of coefficients of polynomials v(n,x) jointly generated with A207622; see the Formula section.

1, 2, 2, 3, 6, 4, 14, 4, 5, 28, 20, 6, 50, 64, 8, 7, 82, 164, 56, 8, 126, 364, 232, 16, 9, 184, 728, 736, 144, 10, 258, 1344, 1968, 736, 32, 11, 350, 2328, 4656, 2800, 352, 12, 462, 3828, 10032, 8800, 2144, 64, 13, 596, 6028, 20064, 24112, 9536, 832, 14

Offset: 1

Author

Clark Kimberling, Feb 20 2012

Keywords

• nonn
• tabl

Comments

Column n is divisible by 2^(n-1); row n ends with 2^(n-1).

Column 2: 2*A004006.

Examples

			First five rows:
1
2...2
3...6
4...14...4
5...28...20
		

Crossrefs

Cf. A207622.

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] + 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[%]    (* A207622 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A207623 *)

Formula

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