|
|
A349269
|
|
Triangle read by rows, T(n, k) = (n - k)! * k! / floor(k / 2)! ^ 2.
|
|
1
|
|
|
1, 1, 1, 2, 1, 2, 6, 2, 2, 6, 24, 6, 4, 6, 6, 120, 24, 12, 12, 6, 30, 720, 120, 48, 36, 12, 30, 20, 5040, 720, 240, 144, 36, 60, 20, 140, 40320, 5040, 1440, 720, 144, 180, 40, 140, 70, 362880, 40320, 10080, 4320, 720, 720, 120, 280, 70, 630
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,4
|
|
COMMENTS
|
Interpolates between the factorial numbers (A000142) and the swinging factorial numbers (A056040).
The identity T(n, 0) = T(n, n)*T(floor(n/2), 0)^2 was investigated as a basis for an efficient implementation of the computation of the factorial numbers (see link).
|
|
LINKS
|
|
|
FORMULA
|
T(n, k) divides T(n, 0) for 0 <= k <= n.
Product_{k=0..n} T(n, k) is a square.
|
|
EXAMPLE
|
[0] 1;
[1] 1, 1;
[2] 2, 1, 2;
[3] 6, 2, 2, 6;
[4] 24, 6, 4, 6, 6;
[5] 120, 24, 12, 12, 6, 30;
[6] 720, 120, 48, 36, 12, 30, 20;
[7] 5040, 720, 240, 144, 36, 60, 20, 140;
[8] 40320, 5040, 1440, 720, 144, 180, 40, 140, 70;
[9] 362880, 40320, 10080, 4320, 720, 720, 120, 280, 70, 630;
|
|
MAPLE
|
T := (n, k) -> (n - k)!*k! / iquo(k, 2)! ^ 2:
seq(seq(T(n, k), k = 0..n), n = 0..9);
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|