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 A052787 A simple grammar. Product of 5 consecutive integers. 16
 0, 0, 0, 0, 0, 120, 720, 2520, 6720, 15120, 30240, 55440, 95040, 154440, 240240, 360360, 524160, 742560, 1028160, 1395360, 1860480, 2441880, 3160080, 4037880, 5100480, 6375600, 7893600, 9687600, 11793600, 14250600, 17100720, 20389320 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 COMMENTS For n>5: a(n) = A173333(n,n-5). - Reinhard Zumkeller, Feb 19 2010 Appears in Harriot along with the formula (for a different offset) a(n) = n^5 + 10n^4 + 35n^3 + 50n^2 + 24n, see links. - Charles R Greathouse IV, Oct 22 2014 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 Thomas Harriot, Manuscript 6782, p. 77, c. 1599. INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 744 Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1). FORMULA a(n) = n*(n-1)*(n-2)*(n-3)*(n-4)=n!/(n-5)!. E.g.f.: x^5*exp(x). Recurrence: {a(1)=0, a(2)=0, a(4)=0, a(3)=0, (-1-n)*a(n)+(-4+n)*a(n+1), a(5)=120}. O.g.f.: 120*x^5/(-1+x)^6. - R. J. Mathar, Nov 16 2007 a(n) = a(n-1) + 5*A052762(n). - J. M. Bergot, May 30 2012 MAPLE spec := [S, {B=Set(Z), S=Prod(Z, Z, Z, Z, Z, B)}, labeled]: seq(combstruct[count](spec, size=n), n=0..20); seq(numbperm (n, 5), n=0..31); # Zerinvary Lajos, Apr 26 2007 G(x):=x^5*exp(x): f[0]:=G(x): for n from 1 to 31 do f[n]:=diff(f[n-1], x) od: x:=0: seq(f[n], n=0..31); # Zerinvary Lajos, Apr 05 2009 MATHEMATICA Times@@@(Partition[Range[-4, 35], 5, 1])  (* Harvey P. Dale, Feb 04 2011 *) PROG (MAGMA) [n*(n-1)*(n-2)*(n-3)*(n-4): n in [0..35]]; // Vincenzo Librandi, May 26 2011 (PARI) a(n)=120*binomial(n, 5) \\ Charles R Greathouse IV, Nov 20 2011 CROSSREFS Cf. A002378, A007531, A052762. Equals 120 * C(n, 5) = 120 * A000389(n). Equals 4 * A054559. Sequence in context: A039688 A005820 A300299 * A292970 A052769 A179724 Adjacent sequences:  A052784 A052785 A052786 * A052788 A052789 A052790 KEYWORD easy,nonn AUTHOR encyclopedia(AT)pommard.inria.fr, Jan 25 2000 EXTENSIONS More terms from Henry Bottomley, Mar 20 2000 Formula corrected by Philippe Deléham, Dec 12 2003 STATUS approved

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Last modified October 18 01:01 EDT 2018. Contains 316297 sequences. (Running on oeis4.)