A182923 a(n) = n$ / A055773(n), where n$ denotes the swinging factorial (A056040).

1, 1, 1, 1, 2, 2, 4, 4, 2, 18, 36, 36, 12, 12, 24, 360, 90, 90, 20, 20, 4, 84, 168, 168, 28, 700, 1400, 37800, 5400, 5400, 720, 720, 90, 2970, 5940, 207900, 23100, 23100, 46200, 1801800, 180180, 180180, 17160

Offset

0,5

Comments

a(n) = n$ * P(floor(n/2))/P(n), P(n) primorial number A034386.

A182922(n) / a(n) = A000142(n) / A056040(n) = A180064(n).

Links

Table of n, a(n) for n=0..42.

Maple

swingfact := n -> n! / iquo(n, 2)!^2;
A182923 := n -> swingfact(n) / mul(k, k=select(isprime, [$iquo(n, 2)+1..n])):

Mathematica

sf[n_] := n!/Floor[n/2]!^2;
a[n_] := sf[n]/Numerator[n!/Floor[n/2]!^4];
Table[a[n], {n, 0, 42}] (* Jean-François Alcover, Jun 22 2019 *)

Crossrefs

Cf. A182922, A034386, A055773, A180064.

Sequence in context: A038674 A330639 A339179 * A263856 A090277 A324662

Adjacent sequences: A182920 A182921 A182922 * A182924 A182925 A182926

Keyword

nonn

Author

Peter Luschny, Mar 05 2011

Status

approved