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A298883 Determinant of n X n matrix whose elements are m(i,j) = prime(i)^j. 2
1, 2, 6, 180, 50400, 958003200, 131514679296000, 1352181326649753600000, 112703642894318944282214400000, 903025586371469323704949549301760000000, 2012769637740033870687308804001121075357286400000000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Traces of these matrices are A087480.

LINKS

Robert Israel, Table of n, a(n) for n = 0..35

Wikipedia, Vandermonde matrix

FORMULA

a(n) = Product_{1<=i<=n} prime(i) * Product_{1<=i<j<=n} (prime(j)-prime(i)). - Robert Israel, Jan 29 2018

EXAMPLE

For n=1:

          |2| = 2, then a(1) = 2.

For n=2:

          |2  4| = 6, then a(2) = 6.

          |3  9|

For n=3:

          |2  4   8| = 180, then a(3) = 180.

          |3  9  27|

          |5 25 125|

MAPLE

with(LinearAlgebra):

a:= n-> Determinant(Matrix(n, (i, j)-> ithprime(i)^j)):

seq(a(n), n=0..12);  # Alois P. Heinz, Jan 28 2018

# Alternative:

f:= proc(n) local P;

P:= [seq(ithprime(i), i=1..n)];

convert(P, `*`)*mul(mul(P[j]-P[i], j=i+1..n), i=1..n-1)

end proc:

map(f, [$0..20]); # Robert Israel, Jan 29 2018

MATHEMATICA

a[n_]:=Table[Prime[i]^j, {i, 1, n}, {j, 1, n}];

Table[Det[a[n]], {n, 1, 10}]

PROG

(PARI) a(n) = matdet(matrix(n, n, i, j, prime(i)^j)); \\ Michel Marcus, Jan 28 2018

CROSSREFS

Cf. A080358, A087480, A298903.

Sequence in context: A137532 A072116 A203430 * A252740 A055696 A158096

Adjacent sequences:  A298880 A298881 A298882 * A298884 A298885 A298886

KEYWORD

nonn

AUTHOR

Andres Cicuttin, Jan 28 2018

STATUS

approved

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Last modified January 18 10:33 EST 2022. Contains 350454 sequences. (Running on oeis4.)