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%I #16 Apr 17 2020 23:04:48
%S 1,76,11989,2091817,372713728,66750320449,11970180565381,
%T 2147314732677364,385238046548443177,69115057977256578649,
%U 12399917664600455876068,2224670061782262303745381,399128369515444836686385361,71607684753022827432994707712
%N Number of perfect matchings in graph C_{9} X P_{2n}.
%D Per Hakan Lundow, "Computation of matching polynomials and the number of 1-factors in polygraphs", Research report, No 12, 1996, Department of Math., Umea University, Sweden.
%H Alois P. Heinz, <a href="/A028480/b028480.txt">Table of n, a(n) for n = 0..400</a>
%H Per Hakan Lundow, <a href="http://www.theophys.kth.se/~phl/Text/1factors2.ps.gz">Enumeration of matchings in polygraphs</a>, 1998.
%F G.f.: (x^15 -189*x^14+9585*x^13 -194987*x^12 +1937034*x^11 -10357902*x^10 +31195513*x^9 -53951967*x^8 +53951967*x^7 -31195513*x^6 +10357902*x^5 -1937034*x^4 +194987*x^3 -9585*x^2 +189*x -1) / ( -x^16 +265*x^15 -17736*x^14 +457655*x^13 -5699687*x^12 +38357160*x^11 -146975161*x^10 +327381265*x^9 -427427424*x^8 +327381265*x^7 -146975161*x^6 +38357160*x^5 -5699687*x^4 +457655*x^3 -17736*x^2 +265*x -1). - _Alois P. Heinz_, Dec 10 2013
%F a(n) = 2^n * sqrt(Resultant(U_{2*n}(x/2), T_{9}(i*x/2))), where T_n(x) is a Chebyshev polynomial of the first kind, U_n(x) is a Chebyshev polynomial of the second kind and i = sqrt(-1). - _Seiichi Manyama_, Apr 17 2020
%o (PARI) {a(n) = sqrtint(4^n*polresultant(polchebyshev(2*n, 2, x/2), polchebyshev(9, 1, I*x/2)))} \\ _Seiichi Manyama_, Apr 17 2020
%K nonn,easy
%O 0,2
%A _Per H. Lundow_