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A052787
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A simple grammar. Product of 5 consecutive integers.
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11
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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; internal format)
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OFFSET
| 0,6
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COMMENTS
| For n>5: a(n) = A173333(n,n-5). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Feb 19 2010]
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..1000
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 744
Index to sequences with linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).
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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 (mathar(AT)strw.leidenuniv.nl), Nov 16 2007
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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 (zerinvarylajos(AT)yahoo.com), Apr 26 2007
restart: 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); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 05 2009]
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MATHEMATICA
| Times@@@(Partition[Range[-4, 35], 5, 1]) (* From Harvey P. Dale, Feb 04 2011 *)
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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
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CROSSREFS
| Cf. A002378, A007531, A052762.
Equals 120 * C(n, 5) = 120 * A000389(n).
Equals 4 * A054559.
Sequence in context: A069085 A039688 A005820 * A052769 A179724 A052766
Adjacent sequences: A052784 A052785 A052786 * A052788 A052789 A052790
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KEYWORD
| easy,nonn
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AUTHOR
| encyclopedia(AT)pommard.inria.fr, Jan 25 2000
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EXTENSIONS
| More terms from Henry Bottomley (se16(AT)btinternet.com), Mar 20 2000
Formula corrected by Philippe DELEHAM, Dec 12 2003
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