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%I #13 Oct 12 2023 19:24:36
%S 0,1,0,0,4,4,1,0,0,0,6,36,81,84,36,9,1,0,0,0,0,8,96,560,2000,4788,
%T 7456,7216,4336,1820,560,120,16,1,0,0,0,0,0,10,200,2000,13000,60625,
%U 213880,587750,1269225,2132950,2734300,2628910,1901400,1065675,480150,177100,53130,12650,2300,300,25,1
%N Irregular triangle read by rows: T(n,k) (0 <= k <= n^2) are coefficients of exact wrapping probability for site percolation on an n X n 2D square lattice with periodic boundary conditions. This is for the probability that it wraps in either dimension.
%C The wrapping probability function is Sum_{k=0..n^2} T(n,k)*p^k*(1-p)^(n^2-k).
%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, 0, 4, 4, 1,
%e 0, 0, 0, 6, 36, 81, 84, 36, 9, 1,
%e 0, 0, 0, 0, 8, 96, 560, 2000, 4788, 7456, 7216, 4336, 1820, 560, 120, 16, 1,
%e 0, 0, 0, 0, 0, 10, 200, 2000, 13000, 60625, 213880, 587750, 1269225, 2132950, 2734300, 2628910, 1901400, 1065675, 480150, 177100, 53130, 12650, 2300, 300, 25, 1,
%e ...
%Y Cf. A365940-A365957, A366463-A366467.
%K nonn,tabf
%O 1,5
%A _N. J. A. Sloane_, Oct 12 2023
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