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A370888
a(n) = (n-1)*(2*(n-2)!+1).
7
3, 6, 15, 52, 245, 1446, 10087, 80648, 725769, 7257610, 79833611, 958003212, 12454041613, 174356582414, 2615348736015, 41845579776016, 711374856192017, 12804747411456018, 243290200817664019, 4865804016353280020, 102181884343418880021, 2248001455555215360022, 51704033477769953280023, 1240896803466478878720024
OFFSET
2,1
COMMENTS
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.
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.
a(n) = A275929(n)-2.
REFERENCES
Wallace Lee, Math Miracles, published by Seeman Printery, Durham, N.C., 1950.
LINKS
Aria Chen, Tyler Cummins, Rishi De Francesco, Jate Greene, Tanya Khovanova, Alexander Meng, Tanish Parida, Anirudh Pulugurtha, Anand Swaroop, and Samuel Tsui, Card Tricks and Information, arXiv:2405.21007 [math.HO], 2024. See p. 9.
FORMULA
E.g.f.: 1 + exp(x)*(x - 1) - 2*(x - log(1 - x)). - Stefano Spezia, Jun 06 2024
MATHEMATICA
Table[(k - 1) (2 Factorial[k - 2] + 1), {k, 2, 20}]
CROSSREFS
Sequence in context: A051610 A322851 A230950 * A327437 A267552 A241269
KEYWORD
nonn
AUTHOR
Tanya Khovanova and PRIMES STEP junior group, Mar 05 2024
STATUS
approved