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

%I A182923 #17 Jun 22 2019 09:17:45
%S A182923 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,
%T A182923 700,1400,37800,5400,5400,720,720,90,2970,5940,207900,23100,23100,
%U A182923 46200,1801800,180180,180180,17160
%N A182923 a(n) = n$ / A055773(n), where n$ denotes the swinging factorial (A056040).
%C A182923 a(n) = n$ * P(floor(n/2))/P(n), P(n) primorial number A034386.
%C A182923 A182922(n) / a(n) = A000142(n) / A056040(n) = A180064(n).
%p A182923 swingfact := n -> n! / iquo(n,2)!^2;
%p A182923 A182923 := n -> swingfact(n) / mul(k, k=select(isprime, [$iquo(n,2)+1..n])):
%t A182923 sf[n_] := n!/Floor[n/2]!^2;
%t A182923 a[n_] := sf[n]/Numerator[n!/Floor[n/2]!^4];
%t A182923 Table[a[n], {n, 0, 42}] (* _Jean-François Alcover_, Jun 22 2019 *)
%Y A182923 Cf. A182922, A034386, A055773, A180064.
%K A182923 nonn
%O A182923 0,5
%A A182923 _Peter Luschny_, Mar 05 2011