[seqfan] Re: An integer sequence related to asymptotic behavior of the sine and cosine integrals

[Moses, Peter J. C.]

Hi Vladimir,

Every other term of A003319.

Clear[a];a[0]=0;a[n_]:=a[n]=n!-Sum[k!*a[n-k],{k,1,n-1}];Join[{1},Table[a[2n](-1)^(n-1),{n,113}]];

generates your list.

Best regards,
Peter.

--------------------------------------------------
From: "Vladimir Reshetnikov" <v.reshetnikov at gmail.com>
Sent: Wednesday, May 11, 2016 1:55 AM
To: <seqfan at seqfan.eu>
Subject: [seqfan] An integer sequence related to asymptotic behavior of the 
sine and cosine integrals

> Dear SeqFans,
>
> I found the following sequence related to asymptotic behavior of the sine
> and cosine integrals:
>
> 1, 1, -13, 461, -29093, 2829325, -392743957, 73943424413, -18176728317413, 
> ...
>
> Except a few first terms, all other terms are only conjectures so far
> (I'm not even sure they all are exact integers, although it appears
> so). For more details, see:
>
> h 
> <goog_1462977391>ttp://math.stackexchange.com/q/1780026/19661http://gist.githubusercontent.com/VladimirReshetnikov/c42a99d3e92d9de45bfe9b713459340b/raw/e856b11e561b11fe46363c7acef2cfb5aef6bd7f/Coefficients
>
> Please let me know if you have any ideas how to find a general formula for 
> them.
>
> --ThanksVladimir Reshetnikov
>
> --
> Seqfan Mailing list - http://list.seqfan.eu/
> 

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