Search: id:A052787
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%I A052787
%S A052787 0,0,0,0,0,120,720,2520,6720,15120,30240,55440,95040,154440,240240,
%T A052787 360360,524160,742560,1028160,1395360,1860480,2441880,3160080,4037880,
%U A052787 5100480,6375600,7893600,9687600,11793600,14250600,17100720,20389320
%N A052787 A simple grammar. Product of 5 consecutive integers.
%H A052787 INRIA Algorithms Project, <a href="http://algo.inria.fr/bin/encyclopedia?Search=ECSnb&argsearch=744">
               Encyclopedia of Combinatorial Structures 744</a>
%F A052787 a(n)=n*(n-1)*(n-2)*(n-3)*(n-4)=n!/(n-5)!.
%F A052787 E.g.f.: x^5*exp(x)
%F A052787 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}
%F A052787 a(n)=numbperm(n,5), n>=0 . - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Apr 26 2007
%F A052787 O.g.f.: 120*x^5/(-1+x)^6. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Nov 16 2007
%p A052787 spec := [S,{B=Set(Z),S=Prod(Z,Z,Z,Z,Z,B)},labeled]: seq(combstruct[count](spec,
               size=n), n=0..20);
%p A052787 seq(numbperm (n,5), n=0..31); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Apr 26 2007
%p A052787 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]
%Y A052787 Cf. A002378, A007531, A052762.
%Y A052787 Equals 120 * C(n, 5) = 120 * A000389(n).
%Y A052787 Equals 4 * A054559.
%Y A052787 Sequence in context: A069085 A039688 A005820 this_sequence A052769 A052766 
               A052627
%Y A052787 Adjacent sequences: A052784 A052785 A052786 this_sequence A052788 A052789 
               A052790
%K A052787 easy,nonn
%O A052787 0,6
%A A052787 encyclopedia(AT)pommard.inria.fr, Jan 25 2000
%E A052787 More terms from Henry Bottomley (se16(AT)btinternet.com), Mar 20 2000
%E A052787 Formula corrected by Philippe DELEHAM, Dec 12 2003

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