A213169 a(n) = n! + n + 1.

2, 3, 5, 10, 29, 126, 727, 5048, 40329, 362890, 3628811, 39916812, 479001613, 6227020814, 87178291215, 1307674368016, 20922789888017, 355687428096018, 6402373705728019, 121645100408832020, 2432902008176640021

Offset: 0

Author

Olivier Gérard, Nov 02 2012

Keywords

• nonn
• easy

Comments

Can be used to detect triangular tables whose rows sum to n! when decreased by 1.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• R. C. Castillo, On the Sum of Corresponding Factorials and Triangular Numbers: Runsums, Trapezoids and Politeness, Asia Pacific Journal of Multidisciplinary Research, 3 (2015), 95-101.
• 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. 5.

Crossrefs

Cf. A000142, A038507, A005095.

Programs

Mathematica

Table[n! + n + 1, {n, 0, 20}]

Maxima

A213169(n):=n!+n+1$
makelist(A213169(n),n,0,30); /* Martin Ettl, Nov 03 2012 */