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A001720 n!/24.
(Formerly M3960 N1634)
37
1, 5, 30, 210, 1680, 15120, 151200, 1663200, 19958400, 259459200, 3632428800, 54486432000, 871782912000, 14820309504000, 266765571072000, 5068545850368000, 101370917007360000, 2128789257154560000 (list; graph; refs; listen; history; text; internal format)
OFFSET

4,2

COMMENTS

The asymptotic expansion of the higher-order exponential integral E(x,m=1,n=5) ~ exp(-x)/x*(1 - 5/x + 30/x^2 - 210/x^3 + 1680/x^4 - 15120/x^5 + 151200/x^6 - 1663200/x^7 + ... ) leads to the sequence given above. See A163931 and A130534 for more information. - Johannes W. Meijer, Oct 20 2009

a(n) = A173333(n,4). - Reinhard Zumkeller, Feb 19 2010

a(n) = A245334(n,n-4) / 5. - Reinhard Zumkeller, Aug 31 2014

REFERENCES

Mitrinovic, D. S.; Mitrinovic, R. S.; Tableaux d'une classe de nombres relies aux nombres de Stirling. Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. Fiz. No. 77 1962, 77 pp.

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 4..300

S. Cerdá, A simple scheme to find the solutions to Brocard-Ramanujan Diophantine Equation n! + 1 = m^2, arXiv:1504.06694 [math.NT], 2015.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 264

W. Lang, On generalizations of Stirling number triangles, J. Integer Seqs., Vol. 3 (2000), #00.2.4.

Alexsandar Petojevic, The Function vM_m(s; a; z) and Some Well-Known Sequences, Journal of Integer Sequences, Vol. 5 (2002), Article 02.1.7

Index to divisibility sequences

Index entries for sequences related to factorial numbers

FORMULA

E.g.f.: x^4/(1-x)^5.

MATHEMATICA

a[n_]:=n!/24; (* Vladimir Joseph Stephan Orlovsky, Dec 13 2008 *)

PROG

(MAGMA) [Factorial(n)/24: n in [4..25]]; // Vincenzo Librandi, Jul 20 2011

(PARI) a(n)=n!/24 \\ Charles R Greathouse IV, Jan 12 2012

(Haskell)

a001720 = (flip div 24) . a000142 -- Reinhard Zumkeller, Aug 31 2014

CROSSREFS

Cf. A049459, A051338. a(n)= A049353(n-3, 1) (first column of triangle).

Cf. A245334, A000142.

Sequence in context: A222050 A091122 A029587 * A051829 A260351 A058247

Adjacent sequences:  A001717 A001718 A001719 * A001721 A001722 A001723

KEYWORD

nonn,easy,changed

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified April 27 06:52 EDT 2017. Contains 285508 sequences.