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%I #13 Oct 09 2023 20:42:27
%S 0,1,0,4,8,4,1,0,9,54,132,171,135,84,36,9,1,0,16,192,1040,3340,7104,
%T 10872,13136,13500,11584,8024,4368,1820,560,120,16,1,0,25,550,5750,
%U 37975,177635,625300,1717700,3767900,6698700,9746040,11687850,11647575,9773725,7044650,4449220,2480625,1211300,510150,181900,53630,12675,2300,300,25,1
%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 square 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 0,4,8,4,1,
%e 0,9,54,132,171,135,84,36,9,1,
%e 0,16,192,1040,3340,7104,10872,13136,13500,11584,8024,4368,1820,560,120,16,1,
%e 0,25,550,5750,37975,177635,625300,1717700,3767900,6698700,9746040,11687850,11647575,9773725,7044650,4449220,2480625,1211300,510150,181900,53630,12675,2300,300,25,1,
%e ...
%Y Cf. A365940-A365944.
%K nonn,tabf
%O 1,4
%A _N. J. A. Sloane_, Oct 09 2023
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