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A298883 Determinant of n X n matrix whose elements are m(i,j) = prime(i)^j.

%I A298883 #29 Jul 28 2019 16:43:32
%S A298883 1,2,6,180,50400,958003200,131514679296000,1352181326649753600000,
%T A298883 112703642894318944282214400000,
%U A298883 903025586371469323704949549301760000000,2012769637740033870687308804001121075357286400000000
%N A298883 Determinant of n X n matrix whose elements are m(i,j) = prime(i)^j.
%C A298883 Traces of these matrices are A087480.
%H A298883 Robert Israel, <a href="/A298883/b298883.txt">Table of n, a(n) for n = 0..35</a>
%H A298883 Wikipedia, <a href="https://en.wikipedia.org/wiki/Vandermonde_matrix">Vandermonde matrix</a>
%F A298883 a(n) = Product_{1<=i<=n} prime(i) * Product_{1<=i<j<=n} (prime(j)-prime(i)). - _Robert Israel_, Jan 29 2018
%e A298883 For n=1:
%e A298883           |2| = 2, then a(1) = 2.
%e A298883 For n=2:
%e A298883           |2  4| = 6, then a(2) = 6.
%e A298883           |3  9|
%e A298883 For n=3:
%e A298883           |2  4   8| = 180, then a(3) = 180.
%e A298883           |3  9  27|
%e A298883           |5 25 125|
%p A298883 with(LinearAlgebra):
%p A298883 a:= n-> Determinant(Matrix(n, (i,j)-> ithprime(i)^j)):
%p A298883 seq(a(n), n=0..12);  # _Alois P. Heinz_, Jan 28 2018
%p A298883 # Alternative:
%p A298883 f:= proc(n) local P;
%p A298883 P:= [seq(ithprime(i),i=1..n)];
%p A298883 convert(P,`*`)*mul(mul(P[j]-P[i],j=i+1..n),i=1..n-1)
%p A298883 end proc:
%p A298883 map(f, [$0..20]); # _Robert Israel_, Jan 29 2018
%t A298883 a[n_]:=Table[Prime[i]^j,{i,1,n},{j,1,n}];
%t A298883 Table[Det[a[n]],{n,1,10}]
%o A298883 (PARI) a(n) = matdet(matrix(n, n, i, j, prime(i)^j)); \\ _Michel Marcus_, Jan 28 2018
%Y A298883 Cf. A080358, A087480, A298903.
%K A298883 nonn
%O A298883 0,2
%A A298883 _Andres Cicuttin_, Jan 28 2018