%I #25 Aug 20 2021 03:35:50

%S 1,2,24,1080,120960,33264000,15567552000,12967770816000,

%T 15768809312256000,29377291748732928000,85194146071325491200000,

%U 319563241913541917491200000,1702632952915351336393113600000,11797543730750469409867884134400000,99429698562764956186366527484723200000

%N Permanent of a square matrix M(n) whose general element M_{i,j} is defined by i*prime(j).

%C det(M(0)) = 1, det(M(1)) = 2 and det(M(n)) = 0 for n > 1.

%C The trace of the matrix M(n) is A014285(n).

%C The antitrace of the matrix M(n) is A014148(n).

%C The antidiagonal of the matrix M(n) is the n-th row of the triangle A309131.

%H Vaclav Kotesovec, <a href="/A330087/b330087.txt">Table of n, a(n) for n = 0..36</a>

%e For n = 1 the matrix M(1) is

%e 2

%e with permanent a(1) = 2.

%e For n = 2 the matrix M(2) is

%e 2, 3

%e 4, 6

%e with permanent a(2) = 24.

%e For n = 3 the matrix M(3) is

%e 2, 3, 5

%e 4, 6, 10

%e 6, 9, 15

%e with permanent a(3) = 1080.

%p with(LinearAlgebra):

%p a:= n-> `if`(n=0, 1, Permanent(Matrix(n, (i, j)-> i*ithprime(j)))):

%p seq(a(n), n=0..14); # _Alois P. Heinz_, Dec 04 2019

%t 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]

%o (PARI) a(n) = matpermanent(matrix(n, n, i, j, i*prime(j))); \\ _Michel Marcus_, Dec 04 2019

%Y Cf. A000040, A014148, A014285, A033286, A309131.

%K nonn

%O 0,2

%A _Stefano Spezia_, Dec 01 2019

%E a(0) = 1 prepended by _Michel Marcus_, Dec 04 2019