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%I #27 Mar 03 2024 10:27:34
%S 1,1,233,2131,145601,2332097,106912793,2188978117,82741005829,
%T 1937528668711,65743732590821,1666961188795475,53060477521960000,
%U 1412218550274852671,43242613716069407953,1185802123987680144427,35457442115448212075033,990424779934371836605849
%N Number of perfect matchings in graph P_{12} X P_{n}.
%H Per Hakan Lundow, <a href="http://www.theophys.kth.se/~phl/Text/1factors.pdf">Computation of matching polynomials and the number of 1-factors in polygraphs</a>, Research report, No 12, 1996, Department of Math., Umea University, Sweden.
%H Per Hakan Lundow, <a href="http://www.theophys.kth.se/~phl/Text/1factors2.ps.gz">Enumeration of matchings in polygraphs</a>, 1998.
%H Sergey Perepechko, <a href="/A028474/a028474.pdf">Generation function</a>
%H <a href="/index/Rec#order_64">Index entries for linear recurrences with constant coefficients</a>, signature (1, 1065, 2271, -313647, -581107, 42290089, 46394373, -3142067439, -1204065921, 141122117137, -23552838575, -4048343500561, 2177821303792, 77145898134992, -57692927620568, -1009771490156144, 834602390555152, 9348345877875672, -7534201668856784, -62671184060029400, 44881022619918032, 309385807529385808, -180904763263594728, -1136378367751634480, 495365037290693552, 3121850377815899650, -901764108815772034, -6426469969210271370, 1005943422942920850, 9913854106266511726, -456766693621948514, -11455967606609256194, -456766693621948514, 9913854106266511726, 1005943422942920850, -6426469969210271370, -901764108815772034, 3121850377815899650, 495365037290693552, -1136378367751634480, -180904763263594728, 309385807529385808, 44881022619918032, -62671184060029400, -7534201668856784, 9348345877875672, 834602390555152, -1009771490156144, -57692927620568, 77145898134992, 2177821303792, -4048343500561, -23552838575, 141122117137, -1204065921, -3142067439, 46394373, 42290089, -581107, -313647, 2271, 1065, 1, -1).
%t t[m_, n_] := Product[2*(2 + Cos[2*j*Pi/(m+1)] + Cos[2*k*Pi/(n+1)]), {k, 1, n/2}, {j, 1, m/2}]; a[n_] := N[t[n, 12], 16] // Round; Table[a[n], {n, 1, 15}] (* _Jean-François Alcover_, Dec 20 2012, after A099390 *)
%o (PARI) {a(n) = sqrtint(polresultant(polchebyshev(12, 2, x/2), polchebyshev(n, 2, I*x/2)))} \\ _Seiichi Manyama_, Apr 13 2020
%Y Row 12 of array A099390.
%K nonn
%O 0,3
%A _Per H. Lundow_
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