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A203418 Vandermonde determinant of the first n composite numbers (A002808). 6
1, 2, 16, 240, 11520, 13271040, 254803968000, 15892123484160000, 5126163351050649600000, 89288743527804466888704000000, 50689719717698351557731837542400000000, 125765178831579421305165126665125232640000000000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Each term divides its successor, as in A203419, and each term is divisible by the corresponding superfactorial, A000178(n), as in A203420.

LINKS

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

MATHEMATICA

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

composite = Rest[Rest[Union[t]]] (* A002808 *)

f[j_] := composite[[j]]; z = 20 ;

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}]              (* A203418 *)

Table[v[n + 1]/v[n], {n, 1, z - 1}] (* A203419 *)

Table[v[n]/d[n], {n, 1, 20}]        (* A203420 *)

CROSSREFS

Cf. A203419, A203420, A000040, A002808.

Sequence in context: A206884 A188756 A156495 * A207082 A207176 A217812

Adjacent sequences:  A203415 A203416 A203417 * A203419 A203420 A203421

KEYWORD

nonn

AUTHOR

Clark Kimberling, Jan 02 2012

STATUS

approved

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Last modified August 13 22:26 EDT 2020. Contains 336464 sequences. (Running on oeis4.)