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A053625
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Product of 6 consecutive integers.
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7
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0, 0, 0, 0, 0, 0, 720, 5040, 20160, 60480, 151200, 332640, 665280, 1235520, 2162160, 3603600, 5765760, 8910720, 13366080, 19535040, 27907200, 39070080, 53721360, 72681840, 96909120, 127512000, 165765600, 213127200, 271252800, 342014400
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OFFSET
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0,7
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COMMENTS
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a(n)=A000579(n)*720. - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 26 2007
For n>5: a(n) = A173333(n,n-6). [From Reinhard Zumkeller, Feb 19 2010]
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index to sequences with linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).
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FORMULA
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a(n)=n*(n-1)*(n-2)*(n-3)*(n-4)*(n-5)=n!/(n-6)!=A052787(n)*(n-6)=a(n-1)*n/(n-6). E.g.f. x^6*exp(x)
a(n)=numbperm (n,6), n>=0. - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 26 2007
G.f.: 720*x^6/(1-x)^7. [Colin Barker, Mar 27 2012]
a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5)-7*a(n-6)+a(n-7). Vincenzo Librandi, Apr 28 2012
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MAPLE
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seq(numbperm (n, 6), n=0..31); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 26 2007
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MATHEMATICA
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CoefficientList[Series[720*x^6/(1-x)^7, {x, 0, 30}], x] (* Vincenzo Librandi, Apr 28 2012 *)
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PROG
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(MAGMA) I:=[0, 0, 0, 0, 0, 0, 720]; [n le 7 select I[n] else 7*Self(n-1)-21*Self(n-2)+35*Self(n-3)-35*Self(n-4)+21*Self(n-5)-7*Self(n-6)+Self(n-7): n in [1..30]]; // Vincenzo Librandi, Apr 28 2012
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CROSSREFS
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A002378, A007531, A045619, A052762, A052787.
Sequence in context: A202095 A187290 A218487 * A052793 A179728 A052799
Adjacent sequences: A053622 A053623 A053624 * A053626 A053627 A053628
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KEYWORD
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easy,nonn
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AUTHOR
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Henry Bottomley, Mar 20 2000
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STATUS
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approved
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