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A001720 a(n) = n!/24.
(Formerly M3960 N1634)
44
1, 5, 30, 210, 1680, 15120, 151200, 1663200, 19958400, 259459200, 3632428800, 54486432000, 871782912000, 14820309504000, 266765571072000, 5068545850368000, 101370917007360000, 2128789257154560000, 46833363657400320000, 1077167364120207360000 (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

REFERENCES

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.

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

D. S. Mitrinovic and R. S. Mitrinovic, Tableaux d'une classe de nombres reliés aux nombres de Stirling, Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. Fiz. No. 77 (1962), 1-77.

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. if offset 0: 1/(1-x)^5.

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

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

G(x) = (1 - (1 + x)^(-4)) / 4 = x - 5 x^2/2! + 30 x^3/3! - ..., an e.g.f. for this signed sequence (for n!/4!), is the compositional inverse of H(x) = (1 - 4*x)^(-1/4) - 1 = x + 5 x^2/2! + 45 x^3/3! + ..., an e.g.f. for A007696. Cf. A094638, A001710 (for n!/2!), and A001715 (for n!/3!). Cf. columns of A094587, A173333, and A213936 and rows of A138533. - Tom Copeland, Dec 27 2019

E.g.f.: x^4 / (4! * (1 - x)). - Ilya Gutkovskiy, Jul 09 2021

MATHEMATICA

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

Range[4, 30]!/24 (* Harvey P. Dale, Jul 27 2021 *)

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

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

Cf. A000142, A049459, A051338, A245334.

Cf. A001710, A001715, A007696, A094638.

Cf. A094587, A138533, A173333, A213936.

Sequence in context: A222050 A091122 A029587 * A051829 A323770 A260351

Adjacent sequences:  A001717 A001718 A001719 * A001721 A001722 A001723

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified May 25 10:05 EDT 2022. Contains 354066 sequences. (Running on oeis4.)