A208516 Triangle of coefficients of polynomials u(n,x) jointly generated with A208517; see the Formula section.

1, 1, 1, 1, 2, 3, 1, 3, 6, 7, 1, 4, 9, 15, 17, 1, 5, 12, 24, 39, 41, 1, 6, 15, 34, 66, 100, 99, 1, 7, 18, 45, 98, 178, 256, 239, 1, 8, 21, 57, 135, 276, 478, 653, 577, 1, 9, 24, 70, 177, 395, 772, 1275, 1661, 1393, 1, 10, 27, 84, 224, 536, 1145, 2139, 3383, 4214

Offset

1,5

Links

Table of n, a(n) for n=1..65.

Formula

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

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

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

Example

First five rows:
1
1...1
1...2...3
1...3...6...7
1...4...9...15...17
First five polynomials u(n,x):
1
1 + x
1 + 2x + 3x^2
1 + 3x + 6x^2 + 7x^3
1 + 4x + 9x^2 + 15x^3 + 17x^4

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := u[n - 1, x] + x*v[n - 1, x];
v[n_, x_] := x*u[n - 1, x] + 2 x*v[n - 1, x] + 1;
Table[Expand[u[n, x]], {n, 1, z/2}]
Table[Expand[v[n, x]], {n, 1, z/2}]
cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
TableForm[cu]
Flatten[%]  (* A208516 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]  (* A208517 *)

Crossrefs

Cf. A208517.

Sequence in context: A209569 A368158 A176850 * A111808 A247046 A081422

Adjacent sequences: A208513 A208514 A208515 * A208517 A208518 A208519

Keyword

nonn,tabl

Author

Clark Kimberling, Feb 28 2012

Status

approved