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Product{k|n} k$. Here '$' denotes the swinging factorial function (A056040).
2

%I #5 Jul 26 2013 04:46:56

%S 1,1,2,6,12,30,240,140,840,3780,15120,2772,221760,12012,960960,

%T 9266400,10810800,218790,7351344000,923780,16761064320,3259095840,

%U 3910915008,16224936,41977154419200,2028117000,249864014400

%N Product{k|n} k$. Here '$' denotes the swinging factorial function (A056040).

%H Peter Luschny, <a href="http://www.luschny.de/math/primes/SwingingPrimes.html"> Swinging Primes.</a>

%e The set of positive divisors of 3 is {1,3}. Thus a(3) = 1$ * 3$ = 1 * 6 = 6.

%p a := proc(n) local i; mul(i,i=map(swing,numtheory[divisors](n))) end:

%t sf[n_] := With[{f = Floor[n/2]}, Pochhammer[f+1, n-f]/f!]; a[0] = 1; a[n_] := Product[sf[k], {k, Divisors[n]}]; Table[a[n], {n, 0, 26}] (* _Jean-François Alcover_, Jul 26 2013 *)

%Y Cf. A098710, A163088, A163089.

%K nonn

%O 0,3

%A _Peter Luschny_, Jul 21 2009