|
|
A249755
|
|
Triangular array of coefficients of polynomials p(n,x) = (x + 1)*p(n-1,x) + (n + 1)*x, p(0,x) = 1.
|
|
4
|
|
|
1, 1, 3, 1, 7, 3, 1, 12, 10, 3, 1, 18, 22, 13, 3, 1, 25, 40, 35, 16, 3, 1, 33, 65, 75, 51, 19, 3, 1, 42, 98, 140, 126, 70, 22, 3, 1, 52, 140, 238, 266, 196, 92, 25, 3, 1, 63, 192, 378, 504, 462, 288, 117, 28, 3, 1, 75, 255, 570, 882, 966, 750, 405, 145, 31
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
COMMENTS
|
(Sum of numbers in row n) = A000295(n+1) for n >= 0.
|
|
LINKS
|
|
|
EXAMPLE
|
p(0,x) = 1
p(1,x) = 1 + 3*x
p(2,x) = 1 + 7*x + 3*x^2
First 6 rows:
1
1 3
1 7 3
1 12 10 3
1 18 22 13 3
1 25 40 35 16 3
|
|
MATHEMATICA
|
z = 14; p[n_, x_] := (x + 1) p[n - 1, x] + (n + 1)*x; p[0, x_] = 1;
t = Table[Factor[p[n, x]], {n, 0, z}]
TableForm[Rest[Table[CoefficientList[t[[n]], x], {n, 0, z}]]] (* A249755 array *)
Flatten[CoefficientList[t, x]] (* A249755 sequence *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|