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

Vladimir Reshetnikov v.reshetnikov at gmail.com
Thu May 12 20:16:07 CEST 2016


Thanks, Peter!
This is a great observation. Any ideas how it can be proved? Are there any
connections between the sine integral and this combinatorial problem?

--
Thanks
Vladimir

On Wed, May 11, 2016 at 4:54 AM, Moses, Peter J. C. <
mows at mopar.freeserve.co.uk> wrote:

> 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
>>
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>> Seqfan Mailing list - http://list.seqfan.eu/
>>
>>
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