A207625 Triangle of coefficients of polynomials u(n,x) jointly generated with A207626; see the Formula section.

1, 2, 4, 3, 7, 12, 3, 11, 32, 21, 3, 16, 70, 83, 30, 3, 22, 135, 247, 161, 39, 3, 29, 238, 616, 622, 266, 48, 3, 37, 392, 1358, 1946, 1276, 398, 57, 3, 46, 612, 2730, 5244, 4854, 2290, 557, 66, 3, 56, 915, 5106, 12630, 15622, 10312, 3745, 743, 75, 3, 67

Offset

1,2

Links

Table of n, a(n) for n=1..57.

Formula

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

v(n,x)=2x*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
4....3
7....12...3
11...32...21...3

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_] := 2 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[%]    (* A207625 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A207626 *)

Crossrefs

Cf. A207626.

Sequence in context: A223625 A166017 A257504 * A238953 A238964 A035507

Adjacent sequences: A207622 A207623 A207624 * A207626 A207627 A207628

Keyword

nonn,tabf

Author

Clark Kimberling, Feb 21 2012

Status

approved