[seqfan] Re: definition of double factorial

Richard Mathar mathar at strw.leidenuniv.nl
Tue Oct 20 13:41:09 CEST 2009

kap> Return-Path: <seqfan-bounces at list.seqfan.eu>
kap> Date: Tue, 20 Oct 2009 12:35:40 +0200
kap> From: Karol <penson at lptl.jussieu.fr>
kap> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>, penson at lptl.jussieu.fr
kap> Subject: [seqfan]  definition of double factorial
kap> This is to inform you that the definition of double factorial numbers
kap>   as given in A001147(n) and  in related sequences as A001818(n)  etc.  
kap> disagrees with Maple's
kap>     function doublefactorial(n). I do not know if this point was raised 
kap> before.
kap>   As this may lead to inconsistencies  I intend to submit a comment on it.
kap>              Karol A.Penson

There is no disagreement. A001147 and A001818 are related to double factorial
numbers doublefactorial(2*n-1). The definition says "Double factorial
numbers: (2n-1)!!" and that this is a bisection of the double factorial
numbers seems to be so obvious from the text (which says 2n-1, not n) that
this cannot lead to confusion, I think. Again, A000165 also says
"Double factorial numbers: (2n)!!", and it seems obvious that this is
the other bisection. To avoid confusion and not to cause panic, I propose
not to add a comment on this besides adding the Maple programs like

%p A000165 A000165 := proc(n) doublefactorial(2*n) ; end:

%p A001147 A001147 := proc(n) doublefactorial(2*n-1) ; end:

%p A001818 A001818 := proc(n) (A001147(n))^2 ; end:

because experience in the past has shown that not all Maple users are
aware of the existence of this Maple function in the standard library.

Richard Mathar

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