[seqfan] Re: A013538

[Simon Plouffe]

Hello,

  me too, I took that example of A013538 and could not
figure out what it was, the term 111 is 37*3 that does
not fit with the first coefficients, unless there is
something to do with (a-1)/2, since a 73 appears in
the first terms but this is just a plain guess.

bonne journée

  Simon Plouffe



Le 17/12/2011 07:24, N. J. A. Sloane a écrit :
> Dear Seq Fans,
> I agree that there are a lot of errors in Patrick Demichel's
> sequences from May 1996.
>
> This is very bad.
>
> 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
>
>
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