%I #13 Oct 12 2023 19:22:56
%S 0,1,0,0,0,4,1,0,0,0,0,0,9,42,36,9,1,0,0,0,0,0,0,0,16,328,1504,2960,
%T 2992,1668,560,120,16,1,0,0,0,0,0,0,0,0,0,25,1510,16300,86925,285200,
%U 625550,947740,1004400,754775,412250,168450,52620,12650,2300,300,25,1
%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 both dimensions.
%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, 0, 4, 1,
%e 0, 0, 0, 0, 0, 9, 42, 36, 9, 1,
%e 0, 0, 0, 0, 0, 0, 0, 16, 328, 1504, 2960, 2992, 1668, 560, 120, 16, 1,
%e 0, 0, 0, 0, 0, 0, 0, 0, 0, 25, 1510, 16300, 86925, 285200, 625550, 947740, 1004400, 754775, 412250, 168450, 52620, 12650, 2300, 300, 25, 1,
%e ...
%Y Cf. A365940-A365957, A366463-A366467.
%K nonn,tabf
%O 1,6
%A _N. J. A. Sloane_, Oct 12 2023