|
|
A349479
|
|
Irregular triangle read by rows: T(n,k) = S1(n,k)*2^k, where S1(n,k) is the associated Stirling number of the first kind (cf. A008306) (n >= 0, 0 <= k <= floor(n/2)).
|
|
0
|
|
|
1, 0, 0, 2, 0, 4, 0, 12, 12, 0, 48, 80, 0, 240, 520, 120, 0, 1440, 3696, 1680, 0, 10080, 29232, 19040, 1680, 0, 80640, 256896, 211456, 40320, 0, 725760, 2493504, 2429280, 705600, 30240, 0, 7257600, 26547840, 29430720, 11285120, 1108800, 0, 79833600, 307992960, 378595008, 177580480, 27720000, 665280
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,4
|
|
COMMENTS
|
T(n,k) is the number of cycle-colored n-derangements possessing exactly k cycles; two colors are available.
|
|
LINKS
|
|
|
EXAMPLE
|
Triangle begins:
[0] 1;
[1] 0;
[2] 0, 2;
[3] 0, 4;
[4] 0, 12, 12;
[5] 0, 48, 80;
[6] 0, 240, 520, 120;
[7] 0, 1440, 3696, 1680;
[8] 0, 10080, 29232, 19040, 1680;
[9] 0, 80640, 256896, 211456, 40320;
...
|
|
MAPLE
|
b:= proc(n) option remember; expand(`if`(n=0, 1, add(
2*x*b(n-j)*binomial(n-1, j-1)*(j-1)!, j=2..n)))
end:
T:= n-> (p-> seq(coeff(p, x, i), i=0..floor(n/2)))(b(n)):
|
|
MATHEMATICA
|
S1[0, 0] = 1; S1[_, 0] = 0; S1[n_, k_] /; k > Quotient[n, 2] = 0;
S1[n_, k_] := S1[n, k] = (n-1)*(S1[n-1, k] + S1[n-2, k-1]);
T[n_, k_] := S1[n, k]*2^k;
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,tabf
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|