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A250104
Triangle read by rows: T(n,k) = number of partitions of n with k circular successions (n>=0, 0 <= k <= n).
4
0, 1, 0, 1, 0, 1, 1, 3, 0, 1, 4, 4, 6, 0, 1, 11, 20, 10, 10, 0, 1, 41, 66, 60, 20, 15, 0, 1, 162, 287, 231, 140, 35, 21, 0, 1, 715, 1296, 1148, 616, 280, 56, 28, 0, 1, 3425, 6435, 5832, 3444, 1386, 504, 84, 36, 0, 1, 17722, 34250, 32175, 19440, 8610, 2772, 840, 120, 45, 0, 1
OFFSET
0,8
LINKS
T. Mansour, A. O. Munagi, Set partitions with circular successions, European Journal of Combinatorics, 42 (2014), 207-216.
EXAMPLE
Triangle begins:
0
1, 0,
1, 0, 1,
1, 3, 0, 1,
4, 4, 6, 0, 1,
11, 20, 10, 10, 0, 1,
41, 66, 60, 20, 15, 0, 1,
162, 287, 231, 140, 35, 21, 0, 1,
715, 1296, 1148, 616, 280, 56, 28, 0, 1,
3425, 6435, 5832, 3444, 1386, 504, 84, 36, 0, 1,
17722, 34250, 32175, 19440, 8610, 2772, 840, 120, 45, 0, 1
...
MATHEMATICA
t[n_, k_] := Binomial[n, k]*((-1)^(n-k)+Sum[(-1)^(j-1)*BellB[n-k-j], {j, 1, n-k}]); t[0, 0]=0; t[1, 0]=1; t[1, 1]=0; Table[t[n, k], {n, 0, 10}, {k, 0, n}] // Flatten (* Jean-François Alcover, Dec 09 2014 *)
CROSSREFS
A124323 is an essentially identical triangle, differing only in row 0 and 1.
For columns see A000296, A250105 - A250107.
Sequence in context: A390263 A143949 A124323 * A220421 A352493 A106683
KEYWORD
nonn,tabl
AUTHOR
N. J. A. Sloane, Nov 16 2014
STATUS
approved