A207618 Triangle of coefficients of polynomials u(n,x) jointly generated with A207619; see the Formula section.

1, 2, 3, 3, 4, 7, 6, 5, 12, 17, 12, 6, 18, 34, 40, 24, 7, 25, 58, 91, 92, 48, 8, 33, 90, 173, 234, 208, 96, 9, 42, 131, 295, 489, 584, 464, 192, 10, 52, 182, 467, 906, 1328, 1424, 1024, 384, 11, 63, 244, 700, 1545, 2651, 3496, 3408, 2240, 768, 12, 75, 318

Offset

1,2

Links

Table of n, a(n) for n=1..59.

Formula

u(n,x)=u(n-1,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
2
3...3
4...7....6
5...12...17...12

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*u[n - 1, x] + 2 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[%]    (* A207618 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A207619 *)

Crossrefs

Cf. A207619.

Sequence in context: A184271 A269098 A119795 * A119614 A260167 A035540

Adjacent sequences: A207615 A207616 A207617 * A207619 A207620 A207621

Keyword

nonn,tabf

Author

Clark Kimberling, Feb 20 2012

Status

approved