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A071102 Determinant of KK* where K is Kasteleyn-Percus matrix for fool's diamond of order n.

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%I A071102 #14 Jan 05 2021 03:28:09
%S A071102 1,2,15,384,32625,9085440,8238791743,24233379889152
%N A071102 Determinant of KK* where K is Kasteleyn-Percus matrix for fool's diamond of order n.
%D A071102 J. Propp, Enumeration of matchings: problems and progress, pp. 255-291 in L. J. Billera et al., eds, New Perspectives in Algebraic Combinatorics, Cambridge, 1999 (see Problem 27).
%H A071102 J. Propp, <a href="http://faculty.uml.edu/jpropp/update.pdf">Updated article</a>
%H A071102 J. Propp, Enumeration of matchings: problems and progress, in L. J. Billera et al. (eds.), <a href="http://www.msri.org/publications/books/Book38/contents.html">New Perspectives in Algebraic Combinatorics</a>
%F A071102 Conjecture from _Seiichi Manyama_, Jan 04 2021: (Start)
%F A071102 a(2*n+1) = A340291(n) = 4^(2*n^2) * Product_{1<=j,k<=n} (1 - cos(j*Pi/(2*n+1))^2 * cos(k*Pi/(2*n+1))^2).
%F A071102 a(2*n) = 2 * 4^(2*(n-1)) * A340166(n) = 2 * 4^(2*(n-1)*n) * Product_{1<=j,k<=n-1} (1 - cos(j*Pi/(2*n))^2 * cos(k*Pi/(2*n))^2). (End)
%Y A071102 Cf. A340166, A340291.
%K A071102 nonn,more
%O A071102 1,2
%A A071102 _N. J. A. Sloane_, May 28 2002