OFFSET
1,4
LINKS
R. A. Brualdi and Emeric Deutsch, Adjacent q-cycles in permutations, arXiv:1005.0781 [math.CO], 2010.
FORMULA
G.f. of column k: Sum_{j>=1} j! * x^(j+k-1) / (1+x^k)^(j+1).
T(n,k) = Sum_{j=0..floor(n/k)-1} (-1)^j * (n-(k-1)*(j+1))! / j!.
EXAMPLE
Triangle starts:
1;
0, 1;
3, 2, 1;
8, 4, 2, 1;
45, 18, 6, 2, 1;
264, 99, 22, 6, 2, 1;
1855, 612, 114, 24, 6, 2, 1;
14832, 4376, 696, 118, 24, 6, 2, 1;
PROG
(PARI) T(n, k) = sum(j=0, n\k-1, (-1)^j*(n-(k-1)*(j+1))!/j!);
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Seiichi Manyama, Feb 21 2024
STATUS
approved