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A203415 Vandermonde determinant of the first n nonprimes (A018252). 5
1, 3, 30, 1680, 201600, 87091200, 1103619686400, 275463473725440000, 240529195987579699200000, 1163776461866305616609280000000, 344605941225348705438623229542400000000, 3717059729911125118574880410324812431360000000000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Each term divides its successor, as in A203416, and each term is divisible by the corresponding superfactorial, A000178(n), as in A203417.

LINKS

Table of n, a(n) for n=1..12.

MATHEMATICA

t = Table[If[PrimeQ[k], 0, k], {k, 1, 100}];

nonprime = Rest[Union[t]];

f[j_] := nonprime[[j]]; z = 20;  (* A018252 *)

v[n_] := Product[Product[f[k] - f[j], {j, 1, k - 1}], {k, 2, n}]

d[n_] := Product[(i - 1)!, {i, 1, n}]

Table[v[n], {n, 1, z}]              (* A203415 *)

Table[v[n + 1]/v[n], {n, 1, z - 1}] (* A203416 *)

Table[v[n]/d[n], {n, 1, 20}]        (* A203417 *)

CROSSREFS

Cf. A203416, A203417, A000040, A018252.

Sequence in context: A203478 A012008 A335710 * A203520 A238767 A323819

Adjacent sequences:  A203412 A203413 A203414 * A203416 A203417 A203418

KEYWORD

nonn

AUTHOR

Clark Kimberling, Jan 01 2012

STATUS

approved

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Last modified July 5 00:01 EDT 2020. Contains 335457 sequences. (Running on oeis4.)