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A330287
Permanent of the n-th principal submatrix M(n) of A319840.
4
1, 1, 8, 208, 11488, 1093056, 158972160, 32734095360, 9049229328384, 3230305304002560, 1445344680438005760, 791762592707031859200, 521023492500173338705920, 405448567547957922512240640, 368210800911998093644372377600, 385879616532879866123928993792000, 462151848929747968377341029122048000
OFFSET
0,3
COMMENTS
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.
det(M(0)) = det(M(1)) = 1 and det(M(n)) = 0 for n > 1.
For n > 0, the trace of the matrix M(n) is A001844(n-1).
For n > 0, the antitrace of the matrix M(n) is A005893(n-1).
For n > 1, the super- and subdiagonal sum is A001105(n-1).
LINKS
FORMULA
a(n) ~ c * A238261^n * n!^2 / sqrt(n), where c = 0.0286685259829... - Vaclav Kotesovec, Aug 19 2021
EXAMPLE
For n = 1 the matrix M(1) is
1
with permanent a(1) = 1.
For n = 2 the matrix M(2) is
1, 2
2, 4
with permanent a(2) = 8.
For n = 3 the matrix M(3) is
1, 2, 3
2, 4, 6
3, 6, 8
with permanent a(3) = 208.
PROG
(PARI) tm(n) = matrix(n, n, i, j, if ((i<3) || (j<3), i*j, 2*(i+j)-4));
a(n) = matpermanent(tm(n));
CROSSREFS
KEYWORD
nonn
AUTHOR
Stefano Spezia, Dec 11 2019
STATUS
approved