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%I #5 Feb 04 2022 14:40:33
%S 1,1,0,1,1,2,2,2,3,8,3,3,7,12,40,5,7,13,26,160,1380,9,13,28,61,918,
%T 12940,211164,14,27,61,161,7260,142453,4997155,205331148
%N Triangle read by rows: T(m,n) is the number of simple paths for a Racetrack car (using von Neumann neighborhood) with initial velocity zero, going from one corner to the diagonally opposite corner on an m X n grid, 1 <= n <= m.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Racetrack_(game)">Racetrack</a>
%e Triangle begins:
%e m\n| 1 2 3 4 5 6 7 8
%e ---+-------------------------------------------
%e 1 | 1
%e 2 | 1 0
%e 3 | 1 1 2
%e 4 | 2 2 3 8
%e 5 | 3 3 7 12 40
%e 6 | 5 7 13 26 160 1380
%e 7 | 9 13 28 61 918 12940 211164
%e 8 | 14 27 61 161 7260 142453 4997155 205331148
%Y Cf. A064297, A291896 (column n=1), A351042, A351106, A351109 (main diagonal).
%K nonn,tabl,more
%O 1,6
%A _Pontus von Brömssen_, Feb 01 2022
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