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%I #31 Aug 19 2021 07:23:10
%S 1,1,8,208,11488,1093056,158972160,32734095360,9049229328384,
%T 3230305304002560,1445344680438005760,791762592707031859200,
%U 521023492500173338705920,405448567547957922512240640,368210800911998093644372377600,385879616532879866123928993792000,462151848929747968377341029122048000
%N Permanent of the n-th principal submatrix M(n) of A319840.
%C The matrix M(n) is defined as M[i,j,n] = i*j if i < 3 or j < 3 and M[i,j,n] = 2*(i + j) - 4 otherwise.
%C det(M(0)) = det(M(1)) = 1 and det(M(n)) = 0 for n > 1.
%C For n > 0, the trace of the matrix M(n) is A001844(n-1).
%C For n > 0, the antitrace of the matrix M(n) is A005893(n-1).
%C For n > 1, the super- and subdiagonal sum is A001105(n-1).
%H Vaclav Kotesovec, <a href="/A330287/b330287.txt">Table of n, a(n) for n = 0..35</a>
%F a(n) ~ c * A238261^n * n!^2 / sqrt(n), where c = 0.0286685259829... - _Vaclav Kotesovec_, Aug 19 2021
%e For n = 1 the matrix M(1) is
%e 1
%e with permanent a(1) = 1.
%e For n = 2 the matrix M(2) is
%e 1, 2
%e 2, 4
%e with permanent a(2) = 8.
%e For n = 3 the matrix M(3) is
%e 1, 2, 3
%e 2, 4, 6
%e 3, 6, 8
%e with permanent a(3) = 208.
%o (PARI) tm(n) = matrix(n, n, i, j, if ((i<3) || (j<3), i*j, 2*(i+j)-4));
%o a(n) = matpermanent(tm(n));
%Y Cf. A001105, A001844, A005893, A319840.
%K nonn
%O 0,3
%A _Stefano Spezia_, Dec 11 2019
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