| NAME
|
allocatedTriangle of coefficients of polynomials v(n,x) jointly generated with A209555; see forthe ClarkFormula Kimberlingsection.
|
| DATA
|
1, 2, 1, 2, 3, 1, 3, 4, 4, 1, 3, 8, 7, 5, 1, 4, 9, 17, 11, 6, 1, 4, 15, 22, 31, 16, 7, 1, 5, 16, 43, 46, 51, 22, 8, 1, 5, 24, 50, 102, 86, 78, 29, 9, 1, 6, 25, 86, 130, 212, 148, 113, 37, 10, 1, 6, 35, 95, 250, 296, 400, 239, 157, 46, 11, 1, 7, 36, 150, 295, 626, 610
|
| OFFSET
|
1,2
|
| COMMENTS
|
For a discussion and guide to related arrays, see A208510.
|
| FORMULA
|
u(n,x)=x*u(n-1,x)+v(n-1,x),
v(n,x)=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...1
2...3...1
3...4...4...1
3...8...7...5...1
First three polynomials v(n,x): 1, 2 + x , 2+ 3x + x^2 .
|
| MATHEMATICA
|
u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := x*u[n - 1, x] + v[n - 1, x];
v[n_, x_] := u[n - 1, x] + x*v[n - 1, x] + 1;
Table[Expand[u[n, x]], {n, 1, z/2}]
Table[Expand[v[n, x]], {n, 1, z/2}]
cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
TableForm[cu]
Flatten[%] (* A209555 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A209556 *)
|
| CROSSREFS
|
Cf. A209555, A208510.
|
| KEYWORD
|
allocated
nonn,tabl
|
| AUTHOR
|
Clark Kimberling (ck6(AT)evansville.edu), Mar 10 2012
|
| STATUS
|
approved
editing
|
|