A225658 a(n) = n! + (n+1)! + 3*(n+2)!.

8, 21, 80, 390, 2304, 15960, 126720, 1134000, 11289600, 123742080, 1480550400, 19199980800, 268240896000, 4016428416000, 64163222323200, 1089292748544000, 19583731335168000, 371693362360320000, 7426753498644480000, 155827373623713792000

Offset: 0

Author

R. J. Mathar, May 11 2013

Keywords

• easy
• nonn

Comments

In factorial base representation (A007623) the terms are written as: 110, 311, 3110, 31100, 311000, ... From a(1) = 21 = "311" onwards each term always begins with "311", followed by n-1 zeros. - Antti Karttunen, Sep 24 2016

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Index entries for sequences related to factorial base representation

Crossrefs

Cf. A000142.

Row 3 of A211369, row 16 of A276955 (from a(1)=21 onward).

Programs

Magma

[Factorial(n) +Factorial(n+1)+3*Factorial(n+2): n in [0..20]]; // Vincenzo Librandi, Apr 09 2014

Maple

A225658 := proc(n)
    n!+(n+1)!+3*(n+2)! ;
end proc:

Mathematica

#[[1]]+#[[2]]+3#[[3]]&/@Partition[Range[0,30]!,3,1] (* Harvey P. Dale, Apr 08 2014 *)
Table[CoefficientList[Series[(3x-x^2-8)/(x-1)^3,{x,0,30}], x][[n]](n-1)!,{n,1,30}] (* Benedict W. J. Irwin, Sep 27 2016 *)

Scheme

(define (A225658 n) (+ (A000142 n) (A000142 (+ 1 n)) (* 3 (A000142 (+ 2 n))))) ;; Antti Karttunen, Sep 24 2016

Formula

a(n) = A211369(3,n).

3*a(n) -(3*n+5)*a(n-1) +(1-n)*a(n-2) +(2-n)*a(n-3) = 0.

E.g.f: (3*x-x^2-8)/(x-1)^3. - Benedict W. J. Irwin, Sep 27 2016