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A001730 n!/6!.
(Formerly M4436 N1876)
23
1, 7, 56, 504, 5040, 55440, 665280, 8648640, 121080960, 1816214400, 29059430400, 494010316800, 8892185702400, 168951528345600, 3379030566912000, 70959641905152000, 1561112121913344000, 35905578804006912000 (list; graph; refs; listen; history; text; internal format)
OFFSET

6,2

COMMENTS

The asymptotic expansion of the higher-order exponential integral E(x,m=1,n=7) ~ exp(-x)/x*(1 - 7/x + 56/x^2 - 504/x^3 + 5040/x^4 - 55440/x^5 + 665280/x^6 - 8648640/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,6). - Reinhard Zumkeller, Feb 19 2010

a(n) = A245334(n,n-6) / 7. - Reinhard Zumkeller, Aug 31 2014

REFERENCES

Mitrinovic, D. S.; Mitrinovic, R. S.; Tableaux d'une classe de nombres relies aux nombres de Stirling. II. Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. Fiz. No. 107-108 1963 1-77.

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 = 6..300

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 266

Index to divisibility sequences

Index entries for sequences related to factorial numbers

FORMULA

E.g.f.: x^6/(1-x)^7.

G.f.: G(0)/2, where G(k)= 1 + 1/(1 - x*(k+7)/(x*(k+7) + 1/G(k+1))); (continued fraction). - Sergei N. Gladkovskii, Jun 06 2013

MATHEMATICA

a[n_]:=n!/6!; Array[a, 4!, 6] (* Vladimir Joseph Stephan Orlovsky, Oct 25 2009 *)

PROG

(MAGMA) [Factorial(n)/720: n in [6..25]]; // Vincenzo Librandi, Jul 20 2011

(PARI) a(n)=n!/720 \\ Charles R Greathouse IV, Jan 12 2012

(Haskell)

a001730 = (flip div 720) . a000142 -- Reinhard Zumkeller, Aug 31 2014

CROSSREFS

Cf. A051338, A051379. a(n)= A051339(n-6, 0)*(-1)^n (first unsigned column of triangle).

Cf. A245334, A000142.

Sequence in context: A165322 A082305 A144263 * A087751 A099345 A245249

Adjacent sequences:  A001727 A001728 A001729 * A001731 A001732 A001733

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified December 18 13:05 EST 2014. Contains 252157 sequences.