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

1,2

Comments

Column 1: Fibonacci numbers, A000045.

Links

Table of n, a(n) for n=1..63.

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.

Example

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

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 *)

Crossrefs

Cf. A207631.

Sequence in context: A367467 A333937 A325785 * A175503 A333389 A352286

Adjacent sequences: A207629 A207630 A207631 * A207633 A207634 A207635

Keyword

nonn,tabl

Author

Clark Kimberling, Feb 23 2012

Status

approved