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Search: id:A052762
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| A052762 |
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A simple grammar. Product of 4 consecutive integers. |
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+0
9
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| 0, 0, 0, 0, 24, 120, 360, 840, 1680, 3024, 5040, 7920, 11880, 17160, 24024, 32760, 43680, 57120, 73440, 93024, 116280, 143640, 175560, 212520, 255024, 303600, 358800, 421200, 491400, 570024, 657720, 755160, 863040, 982080, 1113024
(list; graph; listen)
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OFFSET
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0,5
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COMMENT
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Also, starting with n=4, the square of area of cyclic quadrilateral with sides n, n-1, n-2, n-3. - Zak Seidov (zakseidov(AT)yahoo.com), Jun 20 2003
a(n) + 1 = A062938(n-4) for n>4. - Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Dec 13 2003
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LINKS
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INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 719
Eric WeissteinCyclicQuadrilateral
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FORMULA
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a(n)=n*(n-1)*(n-2)*(n-3)=n!/(n-4)!.
E.g.f.: x^4*exp(x). Recurrence: {a(1)=0, a(2)=0, a(3)=0, a(4)=24, (-1-n)*a(n)+(n-3)*a(n+1)}
a(n)=numbperm (n,4), n>=0 - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 26 2007
O.g.f.: -24*x^4/(-1+x)^5 . - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 23 2007
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MAPLE
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spec := [S, {B=Set(Z), S=Prod(Z, Z, Z, Z, B)}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
seq(numbperm (n, 4), n=0..34); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 26 2007
restart: G(x):=x^4*exp(x): f[0]:=G(x): for n from 1 to 34 do f[n]:=diff(f[n-1], x) od: x:=0: seq(f[n], n=0..34); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 05 2009]
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CROSSREFS
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Cf. A002378, A007531, A052787.
A001094(n) - n.
Sequence in context: A114200 A069074 A059775 this_sequence A099317 A052760 A052754
Adjacent sequences: A052759 A052760 A052761 this_sequence A052763 A052764 A052765
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KEYWORD
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easy,nonn
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AUTHOR
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encyclopedia(AT)pommard.inria.fr, Jan 25 2000
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EXTENSIONS
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More terms from Henry Bottomley (se16(AT)btinternet.com), Mar 20 2000
Formula corrected by Philippe DELEHAM, Dec 12 2003
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