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%I #8 Feb 16 2025 08:34:04
%S 0,1,1,6,12,6,30,129,129,30,160,1984,4536,1984,160,975,45945,310542,
%T 310542,45945,975,6846,1524156,38298270,111933456,38298270,1524156,
%U 6846
%N Array read by antidiagonals: T(m,n) is the number of (undirected) paths in the rook graph K_m X K_n.
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GraphPath.html">Graph Path</a>.
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RookGraph.html">Rook Graph</a>.
%e Array begins:
%e ==============================================
%e m\n| 1 2 3 4 5 ...
%e ---+------------------------------------------
%e 1 | 0 1 6 30 160 ...
%e 2 | 1 12 129 1984 45945 ...
%e 3 | 6 129 4536 310542 38298270 ...
%e 4 | 30 1984 310542 111933456 ...
%e 5 | 160 45945 38298270 ...
%e ...
%Y Main diagonal is A288967.
%Y Rows 1..2 are A038155, A360878.
%Y Cf. A269562, A269565, A286418, A360851, A360855.
%K nonn,tabl,more
%O 1,4
%A _Andrew Howroyd_, Feb 25 2023