Limit looks like

                                   1/2 exp(1)

                                          2
                                (n + 1) (n  - n + 1)
                          Hyper(--------------------)
                                   2   2
                                  n  (n  + n + 1)

                                       n + 1
                              1/2 ---------------
                                    2
                                  (n  + n + 1) n!