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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.

%I A342307 #15 Mar 18 2021 07:11:36
%S A342307 126,936,2520,3780,41184,25200,11160,287280,1029600,151200,27090,
%T A342307 1294560,12927600,18532800,529200,57456,4442760,90619200,439538400,
%U A342307 259459200,846720,110376,12640320,444276000,4893436800,12307075200,2905943040,0,196560,31346784,1706443200,34653528000,222651374400,295369804800,26153487360,0
%N 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.
%H A342307 Vladislav Taranchuk, <a href="https://cpb-us-w2.wpmucdn.com/sites.udel.edu/dist/b/8131/files/2020/12/K_gons_12_7_2020-1.pdf">On the number of k-gons in finite projective planes</a>, (2020).
%F A342307 T(n, k) = k!*binomial(k - 1, 2)*binomial(n^2 + n + 1, k - 1)*(n - 1).
%e A342307 n\k |     3        4         5           6
%e A342307 ----+-------------------------------------
%e A342307   2 |   126     2520     25200      151200 ...
%e A342307   3 |   936    41184   1029600    18532800 ...
%e A342307   4 |  3780   287280  12927600   439538400 ...
%e A342307   5 | 11160  1294560  90619200  4893436800 ...
%e A342307 ...
%t A342307 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
%Y A342307 Cf. A000142, A000217, A000794, A001231, A124278, A124287, A293819.
%K A342307 nonn,tabl
%O A342307 2,1
%A A342307 _Stefano Spezia_, Mar 08 2021