[seqfan] Re: A005002 inconsistent with wikipedia entry about Stirling numbers of the second kind?
franktaw at netscape.net
franktaw at netscape.net
Wed Oct 29 10:19:57 CET 2008
They are the same. The formula defining A005000 does count
what A006505 is counting.
Two points:
The offset of A005000 is wrong. From the definition, it should
be 0, which matches A006505.
The definition of A005000 is overly elaborate. The polynomials
g_n are not needed (although they are of some independent
interest and should perhaps be added as a table). We can just
set a(0) = 1, and
a(n) = Sum_{k=0}^{n-3} C(n-1,k)*a(k).
(Even keeping the polynomials, there is no need to special
case any n > 0. The cases n=1 and n=2 are the normal
interpretation of an empty sum, and n=3, 4, and 5 are
perfectly normal.)
Franklin T. Adams-Watters
-----Original Message-----
From: Richard Mathar <mathar at strw.leidenuniv.nl>
It ought be possible to show by s.o. with some flexibility in
converting e.g.f's to binomial sums to demonstrate that
(apart from offset) A005000 and A006505 are the same -- this is
just proposed by comparing all the numbers.
Richard
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