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A330087
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Permanent of a square matrix M(n) whose general element M_{i,j} is defined by i*prime(j).
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1
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1, 2, 24, 1080, 120960, 33264000, 15567552000, 12967770816000, 15768809312256000, 29377291748732928000, 85194146071325491200000, 319563241913541917491200000, 1702632952915351336393113600000, 11797543730750469409867884134400000, 99429698562764956186366527484723200000
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OFFSET
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0,2
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COMMENTS
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det(M(0)) = 1, det(M(1)) = 2 and det(M(n)) = 0 for n > 1.
The trace of the matrix M(n) is A014285(n).
The antitrace of the matrix M(n) is A014148(n).
The antidiagonal of the matrix M(n) is the n-th row of the triangle A309131.
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LINKS
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EXAMPLE
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For n = 1 the matrix M(1) is
2
with permanent a(1) = 2.
For n = 2 the matrix M(2) is
2, 3
4, 6
with permanent a(2) = 24.
For n = 3 the matrix M(3) is
2, 3, 5
4, 6, 10
6, 9, 15
with permanent a(3) = 1080.
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MAPLE
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with(LinearAlgebra):
a:= n-> `if`(n=0, 1, Permanent(Matrix(n, (i, j)-> i*ithprime(j)))):
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MATHEMATICA
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M[i_, j_, n_] := i*Prime[j]; a[n_] := If[n==0, 1, Permanent[Table[M[i, j, n], {i, n}, {j, n}]]]; Array[a, 14, 0]
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PROG
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(PARI) a(n) = matpermanent(matrix(n, n, i, j, i*prime(j))); \\ Michel Marcus, Dec 04 2019
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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