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%I #15 Feb 12 2024 13:42:51
%S 1,1,2,59,2493,180932,19939272
%N a(n) is the number of distinct values of the permanent of an n X n Hankel matrix using the first 2*n - 1 prime numbers.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Hankel_matrix">Hankel matrix</a>.
%t a[n_] := CountDistinct[Table[Permanent[HankelMatrix[Join[Drop[per = Part[Permutations[Prime[Range[2 n - 1]]], i], n], {Part[per, n]}], Join[{Part[per, n]}, Drop[per, - n]]]], {i, (2 n - 1) !}]]; Join[{1}, Array[a, 5]]
%o (PARI) a(n) = my(v=[1..2*n-1], list=List()); forperm(v, p, listput(list, matpermanent(matrix(n, n, i, j, prime(p[i+j-1]))));); #Set(list); \\ _Michel Marcus_, Feb 08 2024
%o (Python)
%o from itertools import permutations
%o from sympy import primerange, prime, Matrix
%o def A369952(n): return len({Matrix([p[i:i+n] for i in range(n)]).per() for p in permutations(primerange(prime((n<<1)-1)+1))}) if n else 1 # _Chai Wah Wu_, Feb 12 2024
%Y Cf. A290302, A350939, A350940.
%K nonn,hard,more
%O 0,3
%A _Stefano Spezia_, Feb 06 2024
%E a(6) from _Michel Marcus_, Feb 08 2024