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 A001730 n!/6!. (Formerly M4436 N1876) 21

%I M4436 N1876

%S 1,7,56,504,5040,55440,665280,8648640,121080960,1816214400,

%T 29059430400,494010316800,8892185702400,168951528345600,

%U 3379030566912000,70959641905152000,1561112121913344000,35905578804006912000

%N n!/6!.

%C 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]

%C a(n) = A173333(n,6). [From _Reinhard Zumkeller_, Feb 19 2010]

%D 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.

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

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

%H Vincenzo Librandi, <a href="/A001730/b001730.txt">Table of n, a(n) for n = 6..300</a>

%H INRIA Algorithms Project, <a href="http://algo.inria.fr/ecs/ecs?searchType=1&amp;service=Search&amp;searchTerms=266">Encyclopedia of Combinatorial Structures 266</a>

%H <a href="/index/Di#divseq">Index to divisibility sequences</a>

%H <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a>

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

%t a[n_]:=n!/6!; Array[a,4!,6] [From Vladimir Orlovsky, Oct 25 2009]

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

%o (PARI) a(n)=n!/720 \\ _Charles R Greathouse IV_, Jan 12 2012

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

%K nonn,easy,changed

%O 6,2

%A _N. J. A. Sloane_.

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