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%I #9 Oct 09 2023 20:43:25
%S 0,1,0,4,7,4,1,0,9,45,90,126,126,84,36,9,1,0,16,192,1040,3340,7104,
%T 10872,13136,13500,11584,8024,4368,1820,560,120,16,1,0,25,525,5225,
%U 32725,144390,476025,1214400,2454525,4009875,5420535,6256650,6371225,5810550,4714050,3354100,2064550,1085475,481150,177125,53130,12650,2300,300,25,1
%N Irregular triangle read by rows: T(n,k) (0 <= k <= n^2) are coefficients of cluster density function for site percolation on an n X n 2D triangular lattice with periodic boundary conditions.
%C The cluster density function is (1/n^2)*Sum_{k=0..n^2} T(n,k)*p^k*(1-p)^(n^2-k).
%D S. Mertens, I. Jensen, and R. M. Ziff, Universal features of cluster numbers in percolation, Physical Review E 96 (2017) 052119.
%H Stephan Mertens, <a href="https://wasd.urz.uni-magdeburg.de/mertens/research/percolation/">Percolation</a> (Gives first 7 rows)
%e Triangle begins:
%e 0, 1,
%e 0, 4, 7, 4, 1,
%e 0, 9, 45, 90, 126, 126, 84, 36, 9, 1,
%e 0, 16, 192, 1040, 3340, 7104, 10872, 13136, 13500, 11584, 8024, 4368, 1820, 560, 120, 16, 1,
%e ...
%Y Cf. A365941-A365944.
%K nonn,tabf
%O 1,4
%A _N. J. A. Sloane_, Oct 09 2023
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