[seqfan] Re: The Demichel errors, continued

Olivier Gerard olivier.gerard at gmail.com
Sun Dec 18 01:18:47 CET 2011


On Sun, Dec 18, 2011 at 00:19, N. J. A. Sloane <njas at research.att.com>wrote:

>
> We replace this with two sequences:
> Calculating in Maple, here is what I get:
>
> t1 := arccosh(exp(x) - sin(x));
> t2:=series(%,x,50);
>
>               2         3         4          5    503   6    521    7
>  13    8
> t2 := x + 1/3 x  - 1/18 x  - 1/27 x  - 5/648 x  + ----- x  + ------ x  -
> ----- x  -
>                                                  68040      136080
>  51030
>
>     827    9    1812469    10     44303839    11     9150959    12
> 17949817     13
>    ------ x  - ---------- x   + ------------ x   + ----------- x   +
> ------------- x
>    653184      4849891200       203695430400       43649020800
> 1466607098880
>
> ...
>
> or
>
> 1*x+1/3*x^2-1/18*x^3-1/27
> *x^4-5/648*x^5+503/68040*x^6+521/136080*x^7-13/51030*x^8...
>
>
>
To be precise, in all these sequences (correct or not), Patrick considered
E.g.f.s, so you have to apply the Laplace transform (multiplying by (n+k)!,
k a suitable offset) as I did in my computations if we keep the same
normalization.

Olivier



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