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%I #10 Feb 04 2019 14:14:45
%S 1,1,2,5,16,62,286,1519,9184,62000,463964,3800684,33911424,326678010,
%T 3385261194,37492199549,442541571936,5539379635136,73368335117584,
%U 1024178393797764,15041551052243448,231665680071392900,3736363255881557460,62935656581952683960
%N 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.
%H Alois P. Heinz, <a href="/A144188/b144188.txt">Table of n, a(n) for n = 0..474</a> (first 31 terms from Jan Kristian Haugland)
%F 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).
%K nonn
%O 0,3
%A _Jan Kristian Haugland_, Sep 13 2008
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