A160857 a(n) = Product_{prime r < m = prime(n)} m!/(m-r)!.

1, 6, 1200, 22226400, 10041430291200000, 1113268229944758372925440000, 591370140954797288796906892185462374400000000, 21844691101536229507290449088090992624418999145391456256000000000

Offset

1,2

Links

Table of n, a(n) for n=1..8.

Example

a(1) = 1 (empty product).
a(2) = 6 = 3!/1! as 3 = prime(2) and the only prime less than 3 is 2.

Maple

a:= n-> (m-> mul(`if`(isprime(r), m!/(m-r)!, 1), r=2..m-1))(ithprime(n)):
seq(a(n), n=1..8);  # Alois P. Heinz, Mar 18 2021

Mathematica

mpr[lst_]:=Module[{y=Last[lst], c}, c=y-Most[lst]; Times@@(y!/c!)]; Table[ mpr[ Prime[Range[n]]], {n, 10}] (* Harvey P. Dale, Mar 18 2021 *)

Prog

(PARI) a(n) = prod(i=1, n-1, prime(n)!/(prime(n)-prime(i))!); \\ Michel Marcus, Aug 11 2013

Crossrefs

Cf. A000040.

Sequence in context: A185537 A113159 A159717 * A160005 A172923 A131675

Adjacent sequences: A160854 A160855 A160856 * A160858 A160859 A160860

Keyword

nonn

Author

Pratik Deoghare (psdeoghare(AT)gmail.com), May 28 2009

Extensions

Corrected by Harvey P. Dale, Mar 18 2021

Status

approved