|
|
A208909
|
|
Triangle of coefficients of polynomials u(n,x) jointly generated with A208930; see the Formula section.
|
|
3
|
|
|
1, 1, 2, 1, 6, 6, 1, 10, 20, 16, 1, 14, 42, 68, 44, 1, 18, 72, 172, 220, 120, 1, 22, 110, 344, 648, 696, 328, 1, 26, 156, 600, 1480, 2336, 2160, 896, 1, 30, 210, 956, 2900, 5984, 8128, 6608, 2448, 1, 34, 272, 1428, 5124, 12984, 23056, 27536, 19984
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,3
|
|
COMMENTS
|
For a discussion and guide to related arrays, see A208510.
|
|
LINKS
|
|
|
FORMULA
|
u(n,x)=u(n-1,x)+2x*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
1...2
1...6...6
1...10...20...16
1...14...42...68...44
First five polynomials u(n,x):
1
1 + 2x
1 + 6x + 6x^2
1 + 10x + 20x^2 + 16x^3
1 + 14x + 42x^2 + 68x^3 + 44x^4
|
|
MATHEMATICA
|
u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := u[n - 1, x] + 2 x*v[n - 1, x];
v[n_, x_] := (x + 1)*u[n - 1, x] + 2 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]
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|