A370888 a(n) = (n-1)*(2*(n-2)!+1).

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

Author

Tanya Khovanova and PRIMES STEP junior group, Mar 05 2024

Keywords

• nonn

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

• Michael De Vlieger, Table of n, a(n) for n = 2..450
• 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.

Crossrefs

Cf. A030495, A275929.

Programs

Mathematica

Table[(k - 1) (2 Factorial[k - 2] + 1), {k, 2, 20}]

Formula

E.g.f.: 1 + exp(x)*(x - 1) - 2*(x - log(1 - x)). - Stefano Spezia, Jun 06 2024