|
|
A269947
|
|
Triangle read by rows, Stirling cycle numbers of order 3, T(n,n) = 1, T(n,k) = 0 if k<0 or k>n, otherwise T(n,k) = T(n-1,k-1)+(n-1)^3*T(n-1,k), for n>=0 and 0<=k<=n.
|
|
3
|
|
|
1, 0, 1, 0, 1, 1, 0, 8, 9, 1, 0, 216, 251, 36, 1, 0, 13824, 16280, 2555, 100, 1, 0, 1728000, 2048824, 335655, 15055, 225, 1, 0, 373248000, 444273984, 74550304, 3587535, 63655, 441, 1, 0, 128024064000, 152759224512, 26015028256, 1305074809, 25421200, 214918, 784, 1
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,8
|
|
LINKS
|
|
|
FORMULA
|
T(n,1) = ((n-1)!)^3 for n>=1 (cf. A000442).
T(n,n-1) = (n*(n-1)/2)^2 for n>=1 (cf. A000537).
Row sums: Product_{k=1..n} ((k-1)^3+1) for n>=0 (cf. A255433).
|
|
EXAMPLE
|
Triangle starts:
1,
0, 1,
0, 1, 1,
0, 8, 9, 1,
0, 216, 251, 36, 1,
0, 13824, 16280, 2555, 100, 1,
0, 1728000, 2048824, 335655, 15055, 225, 1.
|
|
MAPLE
|
T := proc(n, k) option remember;
`if`(n=k, 1,
`if`(k<0 or k>n, 0,
T(n-1, k-1) + (n-1)^3*T(n-1, k))) end:
for n from 0 to 6 do seq(T(n, k), k=0..n) od;
|
|
MATHEMATICA
|
T[n_, k_] := T[n, k] = Which[n == k, 1, k < 0 || k > n, 0, True, T[n - 1, k - 1] + (n - 1)^3 T[n - 1, k]];
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|