need help for function

[Pfoertner, Hugo]

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-----Original Message-----
From: Max [mailto:relf at unn.ac.ru] 
Sent: Wednesday, February 16, 2005 08:41
To: Eugene McDonnell
Cc: Number Sequences
Subject: Re: need help for function


Directly in Pari code:

{ d2(n) = if(n%2,n!,n!-(n/2)!) }

{ a(n) = 2*n - 1 + sum(k=3,n,(n+1-k)*d2(k)) }

Max

------------------------

For your function I get the next terms:

 3                                      11
 4                                      41
 5                                     191
 6                                    1055
 7                                    6959
 8                                   53159
 9                                  462239
10                                 4499999
11                                48454559
12                               571409999
13                              7321386239
14                            101249648639
15                           1502852279039
16                          23827244757119
17                         401839065331199
18                        7182224591270399
19                      135607710526041599
20                     2696935204633823999
21                    56349204870451046399
22                  1234002202313836031999
23                 28263671938642197657599
24                675741743408209519641599
25              16834429858208762825625599
26             436284579099614945488588799
27           11744604178759373288919551999
28          327941268390132992046676223999
29         9485899926341208565348048895999
30       283896718396483342773650227199999
31      8781146191044548294707515285503999
32    280409232597386143413838469713919999
33   9235354937815614234051163825422335999
34 313423099682637983172306743137222655999

Hugo

---------------------

Eugene McDonnell wrote:
> I have a sequence:
> 
> n 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
> a(n) 1 3 11 41 191 1055 6959 53159 462239 4499999 48454559 571409999 
> 7321386239 101249648639 1502852279039
> 
> where the second differences d2 are
> 
> n 3 4 5 6 7 8 9 10 11 12 13 14 15
> d2(n) 6 22 120 714 5040 40296 362880 3628680 39916800 479000880 
> 6227020800 87178286160 1307674368000
> 
> which have the property that odd and even d2(o) and d2(e) are o! and e! 
> - (e/2)!
> 
> How does one write a function that will generate sequence a?
> 
> Eugene McDonnell