This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A269562 #23 Feb 16 2025 08:33:30 %S A269562 0,0,0,1,1,1,3,3,3,3,12,30,48,30,12,60,480,1566,1566,480,60,360,12000, %T A269562 126120,284112,126120,12000,360,2520,430920,18153720,122330880, %U A269562 122330880,18153720,430920,2520,20160,21052080,4357332000,112777827840,335750676480,112777827840,4357332000,21052080,20160 %N A269562 Array read by antidiagonals: T(n,m) is the number of Hamiltonian cycles in the rook graph K_n X K_m. %C A269562 Equivalently, the number of rook tours on an n X m lattice. %C A269562 2*T(n,m) is divisible by (n-1)!*(m-1)!. - _Andrew Howroyd_, Feb 08 2021 %H A269562 Andrew Howroyd, <a href="/A269562/b269562.txt">Table of n, a(n) for n = 1..96</a> %H A269562 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HamiltonianCycle.html">Hamiltonian Cycle</a> %H A269562 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RookGraph.html">Rook Graph</a> %F A269562 From _Andrew Howroyd_, Feb 08 2021: (Start) %F A269562 T(n,m) = T(m,n). %F A269562 T(n,1) = (n-1)!/2 for n >= 3. (End) %e A269562 Array begins: %e A269562 ============================================================= %e A269562 n\m | 1 2 3 4 5 %e A269562 ----+-------------------------------------------------------- %e A269562 1 | 0 0 1 3 12 ... %e A269562 2 | 0 1 3 30 480 ... %e A269562 3 | 1 3 48 1566 126120 ... %e A269562 4 | 3 30 1566 284112 122330880 ... %e A269562 5 | 12 480 126120 122330880 335750676480 ... %e A269562 6 | 60 12000 18153720 112777827840 2190773906150400 ... %e A269562 7 | 360 430920 4357332000 ... %e A269562 ... %Y A269562 Column 1 is A001710(n-1) for n >= 3. %Y A269562 Columns 2..4 are A276356, A341498, A341499. %Y A269562 Main diagonal is A269561. %Y A269562 Cf. A269565, A286418. %K A269562 nonn,tabl %O A269562 1,7 %A A269562 _Andrew Howroyd_, Feb 29 2016