The asymtotics for the Apery Sequence

                     n
                   -----
                    \                  2                   2
                     )   binomial(n, k)  binomial(n + k, k)
                    /
                   -----
                   k = 0

                              equals the following

                                                         /              1/2
                                        1/2 n      (3/2) |     3    15 2
0.220043767112643037850689760 (17 + 12 2   )  (1/n)      |1 - --- + -------
                                                         |    4 n    64 n
                                                         \

                     1/2          1/2                                    1/2
        2057     75 2      62917 2        5439       7148379     163053 2
     + ------- - ------- + ---------- - -------- + ----------- - -----------
             2        2            3           3             4            4
       4096 n    256 n     262144 n     16384 n    33554432 n    1048576 n

                                 1/2\
         17012457     185652129 2   |
     - ------------ + --------------|
                  5               5 |
       134217728 n    2147483648 n  /



            Note: The constant in front is a non-rigorous estimate.

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