A144188 a(n)/n! is the probability of guessing "up/down" correctly through a deck of n cards marked 1, 2, ..., n, if one always makes the most probable guess.

1, 1, 2, 5, 16, 62, 286, 1519, 9184, 62000, 463964, 3800684, 33911424, 326678010, 3385261194, 37492199549, 442541571936, 5539379635136, 73368335117584, 1024178393797764, 15041551052243448, 231665680071392900, 3736363255881557460, 62935656581952683960

Offset: 0

Author

Jan Kristian Haugland, Sep 13 2008

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..474 (first 31 terms from Jan Kristian Haugland)

Formula

Let f(0, 0) = 1 and f(n, k) = max{f(n - 1, 0) + ... + f(n - 1, k - 1), f(n - 1, k) + ... + f(n - 1, n - 1)} for 0 <= k <= n. Then a(n) = f(n, 0).