A001730 a(n) = n!/6!. (Formerly M4436 N1876)

1, 7, 56, 504, 5040, 55440, 665280, 8648640, 121080960, 1816214400, 29059430400, 494010316800, 8892185702400, 168951528345600, 3379030566912000, 70959641905152000, 1561112121913344000, 35905578804006912000, 861733891296165888000, 21543347282404147200000

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

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 = 6..300

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 266.

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

Index entries for sequences related to factorial numbers.

Index to divisibility sequences.

Formula

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

E.g.f.: x^6/(6!*(1-x)). [corrected by Alois P. Heinz, Jul 09 2021]

a(n) = A173333(n,6). - Reinhard Zumkeller, Feb 19 2010

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

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

From Amiram Eldar, Jan 15 2023: (Start)

Sum_{n>=6} 1/a(n) = 720*e - 1956.

Sum_{n>=6} (-1)^n/a(n) = 720/e - 264. (End)

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, A051339, A051379.

Cf. A130534, A163931, A173333, A245334, A000142.

Sequence in context: A165322 A082305 A144263 * A259900 A087751 A099345

Adjacent sequences: A001727 A001728 A001729 * A001731 A001732 A001733

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved