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A159083
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Products of 7 consecutive integers.
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5
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0, 0, 0, 0, 0, 0, 0, 5040, 40320, 181440, 604800, 1663200, 3991680, 8648640, 17297280, 32432400, 57657600, 98017920, 160392960, 253955520, 390700800, 586051200, 859541760, 1235591280, 1744364160, 2422728000, 3315312000
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OFFSET
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1,8
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COMMENTS
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For n>7: a(n+1) = A173333(n,n-7). - Reinhard Zumkeller, Feb 19 2010
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LINKS
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Harvey P. Dale, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (8, -28, 56, -70, 56, -28, 8, -1).
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FORMULA
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E.g.f.: x^7*exp(x).
G.f.: 5040*x^8/(1-x)^8. - Colin Barker, Mar 27 2012
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MAPLE
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G(x):=x^7*exp(x): f[0]:=G(x): for n from 1 to 36 do f[n]:=diff(f[n-1], x) od: x:=0: seq(f[n], n=0..33);
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MATHEMATICA
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Table[Times@@(n+Range[0, 6]), {n, -6, 25}] (* or *) LinearRecurrence[{8, -28, 56, -70, 56, -28, 8, -1}, {0, 0, 0, 0, 0, 0, 0, 5040}, 30] (* Harvey P. Dale, Apr 07 2018 *)
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PROG
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(PARI) x='x+O('x^30); concat([0, 0, 0, 0, 0, 0, 0], Vec(5040*x^8/(1-x)^8)) \\ G. C. Greubel, Jun 28 2018
(MAGMA) I:=[0, 0, 0, 0, 0, 0, 0, 5040]; [n le 8 select I[n] else 8*Self(n-1) - 28*Self(n-2) +56*Self(n-3) -70*Self(n-4) +56*Self(n-5) -28*Self(n-6) +8*Self(n-7) -Self(n-8): n in [1..30]]; // G. C. Greubel, Jun 28 2018
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CROSSREFS
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Cf. A052762, A052787, A053625.
Sequence in context: A321843 A226886 A284204 * A179731 A061140 A061122
Adjacent sequences: A159080 A159081 A159082 * A159084 A159085 A159086
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KEYWORD
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nonn,easy
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AUTHOR
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Zerinvary Lajos, Apr 05 2009
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STATUS
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approved
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