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A221879
Triangle T(n,k) read by rows: Number of order-reversing full contraction mappings (of an n-chain) with 1 fixed point and height exactly k.
5
1, 2, 0, 3, 2, 1, 4, 6, 4, 0, 5, 12, 12, 4, 1, 6, 20, 28, 18, 6, 0, 7, 30, 55, 52, 27, 6, 1, 8, 42, 96, 120, 88, 36, 8, 0, 9, 56, 154, 240, 230, 136, 48, 8, 1, 10, 72, 232, 434, 516, 400, 200, 60, 10, 0, 11, 90, 333, 728, 1036, 996, 650, 280, 75, 10, 1
OFFSET
1,2
COMMENTS
Row sums are A059570.
REFERENCES
A. D. Adeshola, V. Maltcev and A. Umar, Combinatorial results for certain semigroups of order-preserving full contraction mappings of a finite chain, (submitted).
FORMULA
T(n, 1) = 1, T(2,2) = 0 and T(n,k) = (n-k+1)*C(n-2,k-1) + T(n-2,k-2) for k > 0.
EXAMPLE
T (4,6) = 6 because there are exactly 6 order-reversing full contraction mappings (of a 4-chain) with 1 fixed point and of height exactly 2, namely: (3222), (2221), (2211), (4433), (4333), (3332).
Triangle starts
1,
2, 0,
3, 2, 1,
4, 6, 4, 0,
5, 12, 12, 4, 1,
6, 20, 28, 18, 6, 0,
7, 30, 55, 52, 27, 6, 1,
8, 42, 96, 120, 88, 36, 8, 0,
9, 56, 154, 240, 230, 136, 48, 8, 1,
10, 72, 232, 434, 516, 400, 200, 60, 10, 0,
11, 90, 333, 728, 1036, 996, 650, 280, 75, 10, 1
...
KEYWORD
nonn,tabl
AUTHOR
Abdullahi Umar, Feb 28 2013
STATUS
approved