login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A054119 a(n) = n! + (n-1)! + (n-2)!. 3
1, 2, 4, 9, 32, 150, 864, 5880, 46080, 408240, 4032000, 43908480, 522547200, 6745939200, 93884313600, 1401079680000, 22317642547200, 377917892352000, 6778983923712000, 128403161542656000, 2560949482291200000, 53645489280294912000, 1177524571957493760000, 27027108408834293760000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

In factorial base representation (A007623) the terms are written as: 1, 10, 20, 111, 1110, 11100, 111000, ... From a(3) = 9 = "111" onward each term begins always with three consecutive 1's, followed by n-3 zeros. - Antti Karttunen, Sep 24 2016

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..300

Index entries for sequences related to factorial base representation

FORMULA

For n>2, a(n) = (n-2)! * n^2. [Gary Detlefs, Aug 01 2009]

a(n) = (n+1)!*(H(n-1)+H(n+1)-H(n-2)-H(n))/2, n>1, where H(n) is the n-th harmonic number. [Gary Detlefs, Oct 04 2011]

E.g.f.: x + 1/(1-x) - x*log(1-x) = x^2/G(0)/2 where G(k) = 1 + (k+2)/(x - x*(k+1)/(x + k + 1 - x^4/(x^3 +(k+2)*(k+3)/G(k+1)))); (continued fraction, 3rd kind, 4-step). - Sergei N. Gladkovskii, Jul 06 2012

G.f. G(0) where G(k) = 1 - x/(1 + x/(1 - x - (k+1)/( k+1 - x/Q))); (continued fraction, 3rd kind, 4-step). - Sergei N. Gladkovskii, Jul 28 2012

For n >= 1, a(n) = A276940(n)/n. - Antti Karttunen, Sep 24 2016

MAPLE

seq(n! + (n+1)! + (n+2)!, n=0..30);

MATHEMATICA

Join[{1, 2}, Table[n!+(n+1)!+(n+2)!, {n, 0, 30}]] (* Vladimir Joseph Stephan Orlovsky, May 19 2011 *)

PROG

(MAGMA) [1, 2], [Factorial(n)+Factorial(n-1)+Factorial(n-2): n in [2..20]]; // Vincenzo Librandi, Oct 05 2011

(Scheme) (define (A054119 n) (if (<= n 1) (+ 1 n) (+ (A000142 n) (A000142 (- n 1)) (A000142 (- n 2))))) ;; Antti Karttunen, Sep 24 2016

CROSSREFS

Cf. A001048, A030495, A108217, A276940.

Equals T(n, 3), array T as in A054115.

Row 6 of A276955 (from a(3)=9 onward).

Sequence in context: A214935 A092329 A053548 * A259490 A274758 A266929

Adjacent sequences:  A054116 A054117 A054118 * A054120 A054121 A054122

KEYWORD

nonn

AUTHOR

Clark Kimberling

EXTENSIONS

Simpler definition from Miklos Kristof, Jun 16 2005

More terms from Antti Karttunen, Sep 24 2016

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 16 21:10 EDT 2019. Contains 328103 sequences. (Running on oeis4.)