%I #22 May 19 2024 11:03:52
%S 1,32,11664,42467328,1562500000000,587312954081280000,
%T 2266101334892340404752384,89927963805390785392395474173952,
%U 36735015407753190053984060991247792275456,154528563849617762057150663767149772800000000000000,6695315138840257072470706538467584763944601124280722177130496
%N Number of spanning trees of the (n,n)-torus grid graph.
%C Main diagonal of array in A212796.
%H Germain Kreweras, <a href="https://doi.org/10.1016/0095-8956(78)90021-7">Complexité et circuits Eulériens dans les sommes tensorielles de graphes</a>, J. Combin. Theory, B 24 (1978), 202-212. See p. 210, Para. 4.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/SpanningTree.html">Spanning Tree</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/TorusGridGraph.html">Torus Grid Graph</a>
%F a(n) ~ Gamma(1/4)^4 * exp(4*G*n^2/Pi) / (16 * Pi^3), where G is Catalan's constant A006752. - _Vaclav Kotesovec_, Feb 14 2021
%t Table[n^2 * Product[4*Sin[j*Pi/n]^2 + 4*Sin[k*Pi/n]^2, {k, 1, n-1}, {j, 1, n-1}], {n, 1, 12}] // Round (* _Vaclav Kotesovec_, Feb 14 2021 *)
%Y Cf. A212796, A340562.
%K nonn
%O 1,2
%A _N. J. A. Sloane_, May 27 2012
%E More terms from _Eric W. Weisstein_, May 10 2017