A330287 - OEIS

%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