A173323 a(n) = 3*n! - 1.

2, 2, 5, 17, 71, 359, 2159, 15119, 120959, 1088639, 10886399, 119750399, 1437004799, 18681062399, 261534873599, 3923023103999, 62768369663999, 1067062284287999, 19207121117183999, 364935301226495999, 7298706024529919999, 153272826515128319999, 3372002183332823039999

Offset: 0

Author

Vincenzo Librandi, Feb 16 2010

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200

Crossrefs

Cf. sequences of the type k*n!-1: A033312 (k=1), A020543 (k=2), this sequence, A173321 (k=4), A173317 (k=5), A173316 (k=6).

Programs

Magma

[3*Factorial(n)-1: n in [0..25]]; // Vincenzo Librandi, Sep 30 2013

Magma

[2] cat [n eq 1 select n+1 else n*Self(n-1)+n-1: n in [1..25] ]; // Vincenzo Librandi, Sep 30 2013

Mathematica

Table[3 n! - 1, {n, 0, 25}] (* Vincenzo Librandi, Sep 30 2013 *)
3*(Range[0,20]!)-1 (* Harvey P. Dale, Oct 27 2015 *)

Formula

a(0)=2, a(n) = n*a(n-1)+n-1. - Vincenzo Librandi, Sep 30 2013

D-finite with recurrence a(n) +(-n-2)*a(n-1) +(2*n-1)*a(n-2) +(-n+2)*a(n-3)=0. - R. J. Mathar, Mar 07 2022

E.g.f.: 3/(1 - x) - exp(x). - Stefano Spezia, Oct 14 2024