[seqfan] more on double factorials/Penson
peter.luschny at googlemail.com
Wed Oct 21 00:39:03 CEST 2009
In the message of Karol A. Penson I read:
> [...] double factorial.
> (Traditionally, this name is used only for the (odd) double
> fact.numbers (esp. in thermodynamics),
> probably because the even version is easily simplified to 2^n (n/2)! )
This is an interesting remark. However, if we look at /interpretations/
of sequences things might have a completely different reason.
From the standpoint of an interpretation the values at even indices
might not be what the Maple function (*) delivers.
A hint what this could be is given by the swinging factorial.
For odd indices the double factorial and the double swinging
factorial coincide for integer values. But for even indices
the double swinging factorial are rational numbers.
More one this different view can be found on
(*) Almost all Maple versions do not include this Maple
function in the standard library, only the recent ones.
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