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

1,2

Comments

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

Column 2: 2*A004006.

Links

Table of n, a(n) for n=1..56.

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.

Example

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

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 *)

Crossrefs

Cf. A207622.

Sequence in context: A185810 A015050 A284222 * A116447 A137757 A210751

Adjacent sequences: A207620 A207621 A207622 * A207624 A207625 A207626

Keyword

nonn,tabl

Author

Clark Kimberling, Feb 20 2012

Status

approved