A207617 Triangle of coefficients of polynomials v(n,x) jointly generated with A207616; see the Formula section.

1, 2, 1, 3, 3, 4, 7, 1, 5, 14, 5, 6, 25, 16, 1, 7, 41, 41, 7, 8, 63, 91, 29, 1, 9, 92, 182, 92, 9, 10, 129, 336, 246, 46, 1, 11, 175, 582, 582, 175, 11, 12, 231, 957, 1254, 550, 67, 1, 13, 298, 1507, 2508, 1507, 298, 13, 14, 377, 2288, 4719, 3718, 1079, 92, 1

Offset

1,2

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

Example

First five rows:
1
2...1
3...3
4...7...1
5...14...5

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] + 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[%]    (* A207616  *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A207617 *)

Crossrefs

Cf. A207616.

Sequence in context: A032215 A117363 A007307 * A141576 A078019 A038071

Adjacent sequences: A207614 A207615 A207616 * A207618 A207619 A207620

Keyword

nonn,tabf

Author

Clark Kimberling, Feb 20 2012

Status

approved