# [seqfan] Re: A013538

N. J. A. Sloane njas at research.att.com
Sat Dec 17 07:24:19 CET 2011

```Dear Seq Fans,
I agree that there are a lot of errors in Patrick Demichel's
sequences from May 1996.

I have written to him.

I found the original files containing the sequences
that he sent me in May 1996. It looks like all the errors so far
are in the first file, Demichel1, which is now called a013538.txt and
I attached it to A013538.

I checked A012001, A013000, A013100, A013500 all
of which are correct, more or less.
I updated these 4 entries in the OEIS.

But A013535, A013536, A013538 and probably many
others are wrong.

I'm hoping that either Patrick can remember what he did,
or else by studying the file a013538.txt (which apparently
has 1572 sequences in it) we can "reverse engineer"
what he did and guess what his mistakes were.

For this one, for example,

%I A013538
%S A013538 1,0,0,1,550,111,1230,43910,387215611,55251677,1288012623642,
%T A013538 173068076674,12030718595112,1149894862124624
%V A013538 -1,0,0,1,550,111,1230,43910,387215611,55251677,1288012623642,
%W A013538 173068076674,12030718595112,1149894862124624
%N A013538 arcsin(cosec(x)-cotanh(x))=-x+1/7!*x^7+550/9!*x^9+111/11!*x^11...
%K A013538 sign
%O A013538 0,5
%A A013538 Patrick Demichel (dml(AT)hpfrcu03.france.hp.com)

, the big question is, what is this function?
-x+1/7!*x^7+550/9!*x^9+111/11!*x^11 +1230*x^13/13! + 43910*x^15/15! ...

I tried taking the sine of it, but did not get anywhere.

One thing we know is that all these sequences are from
a finite set: they are some combination of the trig, hyperbolic,
inverse trig, inverse hyperbolic, exp and log functions,
and roughly speaking only three functions
appear in any sequence - they are "level 3"
functions. Demichel's sequences are an extension
of Ron Hardin's - he had looked at all the "level 2" functions.

If I get any news from Patrick I will post it here.

Neil

```