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A001730
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n!/6!.
(Formerly M4436 N1876)
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21
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1, 7, 56, 504, 5040, 55440, 665280, 8648640, 121080960, 1816214400, 29059430400, 494010316800, 8892185702400, 168951528345600, 3379030566912000, 70959641905152000, 1561112121913344000, 35905578804006912000
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OFFSET
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6,2
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COMMENTS
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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). [From Reinhard Zumkeller, Feb 19 2010]
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REFERENCES
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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).
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LINKS
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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
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FORMULA
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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
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MATHEMATICA
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a[n_]:=n!/6!; Array[a, 4!, 6] [From Vladimir Orlovsky, Oct 25 2009]
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PROG
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(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
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CROSSREFS
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Cf. A051338, A051379. a(n)= A051339(n-6, 0)*(-1)^n (first unsigned column of triangle).
Sequence in context: A165322 A082305 A144263 * A087751 A099345 A110830
Adjacent sequences: A001727 A001728 A001729 * A001731 A001732 A001733
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KEYWORD
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nonn,easy,changed
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AUTHOR
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N. J. A. Sloane.
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STATUS
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approved
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