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

1,2

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

Table of n, a(n) for n=1..24.

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. Tanya Khovanova, Jul 27 2024

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

Mathematica

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

Crossrefs

Cf. A341302, A370888, A371217.

Sequence in context: A121926 A063499 A285381 * A082856 A307140 A254402

Adjacent sequences: A372252 A372253 A372254 * A372256 A372257 A372258

Keyword

nonn

Author

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

Status

approved