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A358157
a(n) is the permanent of the n X n matrix M(n) that is defined by M[i,j] = floor(i*j/3).
2
1, 0, 0, 1, 32, 1422, 146720, 18258864, 3217515264, 910849979232, 316878962588928, 143616562358849280, 90359341652805156864, 68004478547050644357120, 63187026071337208000512000, 75392341069747600992153600000, 104962910849766568886449582080000, 174017685915978467201007058206720000
OFFSET
0,5
COMMENTS
The matrix M(n) is the n-th principal submatrix of the rectangular array A143974.
det(M(0)) = 1, det(M(3)) = -1, and otherwise det(M(n)) = 0.
EXAMPLE
a(5) = 1422:
0 0 1 1 1
0 1 2 2 3
1 2 3 4 5
1 2 4 5 6
1 3 5 6 8
MATHEMATICA
a[n_]:=Permanent[Table[Floor[i j/3], {i, n}, {j, n}]]; Join[{1}, Array[a, 17]]
PROG
(Python)
from sympy import Matrix
def A358157(n): return Matrix(n, n, [i*j//3 for i in range(1, n+1) for j in range(1, n+1)]).per() if n else 1 # Chai Wah Wu, Nov 02 2022
CROSSREFS
Cf. A143974.
Cf. A000212 (matrix element M[n,n]), A181286 (trace of M(n)), A358158 (hafnian of M(2*n)).
Sequence in context: A302806 A303467 A240345 * A300470 A326103 A300809
KEYWORD
nonn
AUTHOR
Stefano Spezia, Nov 01 2022
STATUS
approved