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A342307
Table read by ascending antidiagonals: T(n, k) is the maximum number of quasi k-gons that are not k-gons in a finite projective plane of order n, with k >= 3.
0
126, 936, 2520, 3780, 41184, 25200, 11160, 287280, 1029600, 151200, 27090, 1294560, 12927600, 18532800, 529200, 57456, 4442760, 90619200, 439538400, 259459200, 846720, 110376, 12640320, 444276000, 4893436800, 12307075200, 2905943040, 0, 196560, 31346784, 1706443200, 34653528000, 222651374400, 295369804800, 26153487360, 0
OFFSET
2,1
FORMULA
T(n, k) = k!*binomial(k - 1, 2)*binomial(n^2 + n + 1, k - 1)*(n - 1).
EXAMPLE
n\k | 3 4 5 6
----+-------------------------------------
2 | 126 2520 25200 151200 ...
3 | 936 41184 1029600 18532800 ...
4 | 3780 287280 12927600 439538400 ...
5 | 11160 1294560 90619200 4893436800 ...
...
MATHEMATICA
T[n_, k_]:=k!Binomial[k-1, 2]Binomial[n^2+n+1, k-1](n-1); Table[T[n-k+3, k], {n, 2, 9}, {k, 3, n+1}]//Flatten
KEYWORD
nonn,tabl
AUTHOR
Stefano Spezia, Mar 08 2021
STATUS
approved