A372255 a(1) = 1, a(n) = n*(n-2)! + n - 1.

1, 3, 5, 11, 34, 149, 846, 5767, 45368, 403209, 3991690, 43545611, 518918412, 6706022413, 93405312014, 1394852659215, 22230464256016, 376610217984017, 6758061133824018, 128047474114560019, 2554547108585472020, 53523844179886080021, 1175091669949317120022, 26976017466662584320023

Offset: 1

Author

Tanya Khovanova and the MIT PRIMES STEP junior group, Apr 24 2024

Keywords

• nonn

Comments

Arises from studying a certain card trick.

[In response to a question, the author tells me this is based on Secton 2.3.3 of https://arxiv.org/pdf/2405.21007 . I have asked her to add a link here to that paper, and also to any other sequences mentioned there. - N. J. A. Sloane, Jul 05 2024]

Links

• Michael Kleber and Ravi Vakil, The best card trick, The Mathematical Intelligencer 24 (2002), 9-11.
• Aria Chen, Tyler Cummins, Rishi De Francesco, Jate Greene, Alexander Meng, Tanish Parida, Anirudh Pulugurtha, Anand Swaroop, Samuel Tsui, and Tanya Khovanova, Card Tricks and Information, arXiv 2405.21007 [math.HO], 2024.

Crossrefs

Cf. A341302, A370888, A371217.

Programs

Mathematica

Join[{1},Table[n(n - 2)! + n - 1, {n,2,30}]]

Formula

a(n) = A341302(n-1) + 2 for n > 1.

D-finite with recurrence a(n) +(-n+1)*a(n-1) +(n-4)*a(n-3) +(4*n-13) = 0. - R. J. Mathar, May 24 2024

E.g.f.: 1 + x - exp(x)*(1 - x) - x*log(1 - x). - Stefano Spezia, May 24 2024