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A159083
Products of 7 consecutive integers.
5
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, 4475671200, 5967561600, 7866331200
OFFSET
0,8
LINKS
Michael De Vlieger and Harvey P. Dale, Table of n, a(n) for n = 0..10000 (first 1000 terms by Harvey P. Dale.)
FORMULA
E.g.f.: x^7*exp(x).
For n>=8: a(n) = A173333(n,n-7). - Reinhard Zumkeller, Feb 19 2010
G.f.: 5040*x^7/(1-x)^8. - Colin Barker, Mar 27 2012
From Amiram Eldar, Mar 08 2022: (Start)
a(n) = n*(n-1)*(n-2)*(n-3)*(n-4)*(n-5)*(n-6) = n!/(n-7)!.
Sum_{n>=7} 1/a(n) = 1/4320.
Sum_{n>=7} (-1)^(n+1)/a(n) = 4*log(2)/45 - 1327/21600. (End)
MAPLE
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);
MATHEMATICA
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 *)
PROG
(PARI) my(x='x+O('x^30)); concat([0, 0, 0, 0, 0, 0, 0], Vec(5040*x^7/(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
CROSSREFS
Equals A008279(n,7) (for n>=7).
Sequence in context: A321843 A226886 A284204 * A179731 A061140 A061122
KEYWORD
nonn,easy
AUTHOR
Zerinvary Lajos, Apr 05 2009
STATUS
approved