[seqfan] Re: A191301

Max Alekseyev maxale at gmail.com
Sun Mar 3 23:41:52 CET 2013


Maximilian proposed a natural change in definition making it work for
a(0) as well.
Thanks!
Max

On Sun, Mar 3, 2013 at 4:44 PM, Maximilian Hasler
<maximilian.hasler at gmail.com> wrote:
> note that it's  1+sum(n>0)
> and not sum( n>=0 )
>
> Maximilian
>
>
> On Sun, Mar 3, 2013 at 4:11 PM, Max Alekseyev <maxale at gmail.com> wrote:
>> I agree. The sequence should start with offset 1.
>> Max
>>
>> On Sun, Mar 3, 2013 at 3:08 PM,  <israel at math.ubc.ca> wrote:
>>> I think the problem is with the a(0)=1, which doesn't really fit: for
>>> n >= 1 you take the coefficient of x^(2n) times (2n-1)!, but that doesn't
>>> work for n=0.
>>>
>>> Robert Israel
>>> University of British Columbia
>>>
>>>
>>> On Mar 3 2013, Heinz, Alois wrote:
>>>
>>>>
>>>> seems to be correct:
>>>>
>>>> 1,seq((2*n-1)!*coeff(series(exp(x*arcsin(x)),x,2*n+3),x,2*n), n=1..10);
>>>> gives:
>>>> 1, 1, 4, 49, 1303, 63513, 5044601, 598488981, 99463522845, 22073876512113,
>>>> 6308016788410641
>>>> or
>>>> 1+add(a(n)*x^(2*n)/(2*n-1)!, n=1..5);
>>>> gives
>>>> 1+x^2+2/3*x^4+49/120*x^6+1303/5040*x^8+7057/40320*x^10
>>>> and
>>>> series(exp(x*arcsin(x)), x, 11);
>>>> gives
>>>> 1+x^2+2/3*x^4+49/120*x^6+1303/5040*x^8+7057/40320*x^10+O(x^12)
>>>>
>>>> Best regards, Alois
>>>>
>>>> Am 03.03.2013 13:24, schrieb Harvey P. Dale:
>>>>>
>>>>>         There is something wrong with the definition (Name) of this
>>>>> sequence.
>>>>>         Best,
>>>>>         Harvey
>>>>>
>>>>
>>>>
>>>>
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>>>
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