need help for function

[Eugene McDonnell]

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



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