A207614 Triangle of coefficients of polynomials u(n,x) jointly generated with A207615; see the Formula section.

1, 2, 5, 1, 11, 5, 1, 23, 16, 6, 1, 47, 44, 23, 7, 1, 95, 112, 74, 31, 8, 1, 191, 272, 216, 113, 40, 9, 1, 383, 640, 592, 368, 162, 50, 10, 1, 767, 1472, 1552, 1112, 579, 222, 61, 11, 1, 1535, 3328, 3936, 3184, 1902, 861, 294, 73, 12, 1, 3071, 7424, 9728

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

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

Example

First five rows:
1
2
5....1
11...5....1
23...16...6...1

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_] := u[n - 1, x] + (x + 1)*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[%]    (* A207614 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A207615 *)

Crossrefs

Cf. A207615.

Sequence in context: A323411 A089618 A207629 * A156067 A352577 A263487

Adjacent sequences: A207611 A207612 A207613 * A207615 A207616 A207617

Keyword

nonn,tabf

Author

Clark Kimberling, Feb 20 2012

Status

approved