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%I #6 May 25 2024 21:02:35
%S 1,1,7,1,40,1135,1,216,28942,3329245,1,1144,707239,358911148,
%T 167176484530,1,6016,16963938,37502829018,74568672196498,
%U 140386491543732211,1,31552,403490839,3856945416544,32485805235240376,256258754970108999490,1946586793700869420041631
%N Triangle read by rows: T(n,k) is the number of edge subsets E of the n X k grid graph such that E contains a path between the top left node and the bottom right node, 1 <= k <= n.
%C T(n,k)/2^A151890(n-1,k-1) is the probability that the top left and bottom right vertices of the n X k grid graph are still connected after each edge has been independently deleted with probability 1/2.
%C Terms in the n-th row/column satisfies a linear recurrence with constant coefficients (probably of order A000245(n) or less).
%H Pontus von Brömssen, <a href="/A373036/b373036.txt">Table of n, a(n) for n = 1..55 (rows 1..10)</a>
%e Triangle begins:
%e 1;
%e 1, 7;
%e 1, 40, 1135;
%e 1, 216, 28942, 3329245;
%e 1, 1144, 707239, 358911148, 167176484530;
%e 1, 6016, 16963938, 37502829018, 74568672196498, 140386491543732211;
%e ...
%Y Cf. A000245, A151890, A349594 (2nd row/column), A349596 (3rd row/column) A365629 (4th row/column), A373037 (main diagonal).
%K nonn,tabl
%O 1,3
%A _Pontus von Brömssen_, May 20 2024
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