A207631 Triangle of coefficients of polynomials u(n,x) jointly generated with A207632; see the Formula section.

1, 2, 4, 2, 7, 6, 2, 12, 15, 8, 2, 20, 33, 25, 10, 2, 33, 68, 66, 37, 12, 2, 54, 134, 159, 113, 51, 14, 2, 88, 256, 359, 309, 176, 67, 16, 2, 143, 478, 774, 781, 536, 257, 85, 18, 2, 232, 877, 1611, 1864, 1493, 860, 358, 105, 20, 2, 376, 1587, 3262, 4256

Offset

1,2

Links

Table of n, a(n) for n=1..60.

Formula

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

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

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

Example

First five rows:
1
2
4...2
7...6...2
12...15...8...2

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 + 1)*u[n - 1, x] + 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[%]  (* A207631 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]  (* A207632 *)

Crossrefs

Cf. A207632.

Sequence in context: A228367 A110925 A214789 * A207612 A207620 A354766

Adjacent sequences: A207628 A207629 A207630 * A207632 A207633 A207634

Keyword

nonn,tabf

Author

Clark Kimberling, Feb 23 2012

Status

approved