A207633 Triangle of coefficients of polynomials u(n,x) jointly generated with A207634; see the Formula section.

1, 2, 4, 3, 7, 9, 6, 12, 22, 21, 12, 20, 48, 62, 48, 24, 33, 98, 157, 163, 108, 48, 54, 192, 367, 463, 410, 240, 96, 88, 365, 810, 1203, 1281, 1000, 528, 192, 143, 679, 1715, 2919, 3634, 3392, 2384, 1152, 384, 232, 1242, 3518, 6742, 9550, 10379, 8696

Offset

1,2

Links

Table of n, a(n) for n=1..53.

Formula

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

v(n,x)=(x+1)*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
4....3
7....9....6
12...22...21...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 + 1)*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[%]  (* A207633 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]  (* A207634 *)

Crossrefs

Cf. A207634.

Sequence in context: A246268 A246267 A101267 * A177877 A090568 A329877

Adjacent sequences: A207630 A207631 A207632 * A207634 A207635 A207636

Keyword

nonn,tabf

Author

Clark Kimberling, Feb 24 2012

Status

approved