%I #7 Jul 07 2015 11:51:07
%S 1,-3,-16,60,384,-1680,-12288,60480,491520,-2661120,-23592960,
%T 138378240,1321205760,-8302694400,-84557168640,564583219200,
%U 6088116142080,-42908324659200,-487049291366400,3604299271372800
%N a(n) gives the determinant of a bisymmetric n X n matrix involving the entries 1, 2, ..., A002620(n+1).
%C The maximal number of distinct entries of an n X n bisymmetric matrix B_n is A002620(n+1) = ((n+1)/2)^2 if n is odd and = n*(n+2)/4 if n is even. See a comment and example under A002620.
%C Here the first A002620(n+1) positive numbers are used consecutively, that is B_n[i, j] = (i-1)*n - (i-1)^2 + j for j=i..N-(i-1) and i = 1..ceiling(n/2).
%C Conjecture: a(2*n-1) = (-1)^(n-1)*A034976(n), n >= 1.
%C For a(2*n)/3 see A259057(n), n >= 1 (assuming that a(2*n) is always divisible by 3).
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Bisymmetric_matrix">Bisymmetric Matrix </a>.
%F Determinant of the above defined bisymmetric matrix B_n, n >= 1.
%e n = 1, B_1 [1], a(1) = det(B_1) = 1.
%e n = 2, B_2 = [[1,2],[2,1]], a(2) = det(B_2) = -3.
%e n = 3: B_3 = [[1,2,3],[2,4,2],[3,2,1]], a(3) = det(B_3) = -16
%e n = 4: B_4 = [[1,2,3,4],[2,5,6,3],[3,6,5,2],[4,3,2,1]], a(4) = det(B_4) = 60.
%Y Cf. A002620, A259057.
%K sign,easy
%O 1,2
%A _Wolfdieter Lang_, Jul 07 2015