A173322 a(n) = 4*n! + 1.

5, 5, 9, 25, 97, 481, 2881, 20161, 161281, 1451521, 14515201, 159667201, 1916006401, 24908083201, 348713164801, 5230697472001, 83691159552001, 1422749712384001, 25609494822912001, 486580401635328001, 9731608032706560001, 204363768686837760001, 4496002911110430720001

Offset

0,1

Links

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

Formula

a(n) = n*a(n-1) - n + 1, a(0)=5. - Sergei N. Gladkovskii, Jul 04 2012

From Elmo R. Oliveira, Oct 31 2025: (Start)

a(n) = 4*A000142(n) + 1.

E.g.f.: 4/(1-x) + exp(x). (End)

Maple

a:= proc(n) if n=0 then 5 else a(n) := n*a(n-1)-n+1 fi end: seq (a(n), n=0..25);  # Sergei N. Gladkovskii, Jul 04 2012

Mathematica

4*Range[0, 20]!+1 (* Harvey P. Dale, Jun 26 2012 *)
Table[4 n! + 1, {n, 0, 21}] (* Vincenzo Librandi, Sep 29 2013 *)

Prog

(Magma) [4*Factorial(n) + 1: n in [0..25]]; // Vincenzo Librandi, Sep 29 2013
(Magma) [5] cat [n eq 1 select n+4 else n*Self(n-1)-n+1: n in [1..25] ]; // Vincenzo Librandi, Sep 29 2013

Crossrefs

Cf. sequences of the type k*n!+1: A038507 (k=1), A052898 (k=2), A173324 (k=3), this sequence, A173319 (k=5), A173314 (k=6).

Cf. A000142.

Sequence in context: A147197 A323301 A147047 * A097910 A321655 A336128

Adjacent sequences: A173319 A173320 A173321 * A173323 A173324 A173325

Keyword

nonn,easy

Author

Vincenzo Librandi, Feb 16 2010

Status

approved