This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A372264 #25 Jun 07 2024 02:28:41
%S A372264 1,1,2,15,104,695,5004,40271,362816,3628719,39916700,479001479,
%T A372264 6227020656,87178291031,1307674367804,20922789887775,355687428095744,
%U A372264 6402373705727711,121645100408831676,2432902008176639639,51090942171709439600,1124000727777607679559,25852016738884976639516
%N A372264 a(n) = n! - n^2 + 2n - 1.
%C A372264 The number of distinct cards in a deck that has each card twice to perform the n-card trick, where the assistant chooses the hidden card. This number corresponds to a particular strategy, where if there is a duplicate card, then the assistant puts one of those duplicates on the far left and hides the other. The assistant then arranges all the other cards in nondecreasing order. If there are no duplicates, the strategy is similar to the standard one.
%H A372264 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. 19.
%H A372264 Michael Kleber and Ravi Vakil, <a href="https://web.northeastern.edu/seigen/11Magic/Articles/Best%20Card%20Trick.pdf">The best card trick</a>, The Mathematical Intelligencer 24 (2002), 9-11.
%F A372264 E.g.f.: 1/(1 - x) - exp(x)*(1 - x + x^2). - _Stefano Spezia_, Jun 06 2024
%t A372264 Table[(n! - n^2 + 2 n - 1), {n, 1, 25}]
%o A372264 (Python)
%o A372264 from math import factorial
%o A372264 def A372264(n): return factorial(n)-(n-1)**2 # _Chai Wah Wu_, May 02 2024
%Y A372264 Cf. A370888, A371217, A372255, A372256.
%K A372264 nonn,easy
%O A372264 1,3
%A A372264 _Tanya Khovanova_ and the MIT PRIMES STEP junior group, Apr 24 2024