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

0,3

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).

Crossrefs

Sequence in context: A173469 A138549 A210667 * A157314 A374073 A159603

Adjacent sequences: A144185 A144186 A144187 * A144189 A144190 A144191

Keyword

nonn

Author

Jan Kristian Haugland, Sep 13 2008

Status

approved