[seqfan] Re: A191301

Maximilian Hasler maximilian.hasler at gmail.com
Sun Mar 3 22:44:31 CET 2013


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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>>>
>>>
>>
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