A090115 a(n)=Product[p(n)-j, j=1..n]/n!=A090114(n)/n!.

1, 1, 4, 15, 252, 924, 11440, 43758, 497420, 13123110, 54627300, 1251677700, 12033222880, 52860229080, 511738760544, 10363194502115, 197548686920970, 925029565741050, 17302625882942400, 161884603662657876

Offset

1,3

Comments

It needs proof that A090114(n) is always divisible by n!, that is, these terms are integers.

Links

Table of n, a(n) for n=1..20.

Example

n=5: p(5)=11, a(5)=(11-1)()(11-2)(11-3)(11-4)(11-5)/5!= 10.9.8.7.6/120=30240=252

Mathematica

Table[Apply[Times, Table[Prime[w]-j, {j, 1, w}]]/w!, {w, 1, 15}]

Crossrefs

Cf. A000142, A090114.

Sequence in context: A153060 A139244 A369727 * A051999 A048731 A363351

Adjacent sequences: A090112 A090113 A090114 * A090116 A090117 A090118

Keyword

nonn

Author

Labos Elemer, Jan 08 2004

Status

approved