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%I #28 Jun 06 2024 15:12:44
%S 3,6,15,52,245,1446,10087,80648,725769,7257610,79833611,958003212,
%T 12454041613,174356582414,2615348736015,41845579776016,
%U 711374856192017,12804747411456018,243290200817664019,4865804016353280020,102181884343418880021,2248001455555215360022,51704033477769953280023,1240896803466478878720024
%N a(n) = (n-1)*(2*(n-2)!+1).
%C The maximum deck size to perform the n-card trick using the Fitch Cheney method. This trick is known as the 5-card trick, where the maximum deck size is 52.
%C The method was later improved to serve a bigger deck described by A030495. In particular, the 5-card trick can be performed with the deck of size 124, and this size is the largest possible.
%C a(n) = A275929(n)-2.
%D Wallace Lee, Math Miracles, published by Seeman Printery, Durham, N.C., 1950.
%H Michael De Vlieger, <a href="/A370888/b370888.txt">Table of n, a(n) for n = 2..450</a>
%H Aria Chen, Tyler Cummins, Rishi De Francesco, Jate Greene, Tanya Khovanova, Alexander Meng, Tanish Parida, Anirudh Pulugurtha, Anand Swaroop, and Samuel Tsui, <a href="https://arxiv.org/abs/2405.21007">Card Tricks and Information</a>, arXiv:2405.21007 [math.HO], 2024. See p. 9.
%F E.g.f.: 1 + exp(x)*(x - 1) - 2*(x - log(1 - x)). - _Stefano Spezia_, Jun 06 2024
%t Table[(k - 1) (2 Factorial[k - 2] + 1), {k, 2, 20}]
%Y Cf. A030495, A275929.
%K nonn
%O 2,1
%A _Tanya Khovanova_ and PRIMES STEP junior group, Mar 05 2024
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