%I A007531 M4159
%S A007531 0,0,0,6,24,60,120,210,336,504,720,990,1320,1716,2184,2730,3360,4080,4896,
%T A007531 5814,6840,7980,9240,10626,12144,13800,15600,17550,19656,21924,24360,
%U A007531 26970,29760,32736,35904,39270,42840,46620,50616,54834,59280,63960
%N A007531 n*(n-1)*(n-2) (or n!/(n-3)!).
%C A007531 Ed Pegg Jr (ed(AT)mathpuzzle.com) conjectures that n^3 - n = k! has a 
               solution iff n is 2, 3, 5 or 9 (when k is 3, 4, 5 and 6).
%C A007531 Three-dimensional promic (or oblong) numbers, cf. A002378 - Alexandre 
               Wajnberg (alexandre.wajnberg(AT)skynet.be), Dec 29 2005
%C A007531 Doubled first differences of tritriangular numbers A050534(n) = (1/8)n(n 
               + 1)(n - 1)(n - 2). a(n) = 2*(A050534(n+1) - A050534(n)). - Alexander 
               Adamchuk (alex(AT)kolmogorov.com), Apr 11 2006
%C A007531 If Y is a 4-subset of an n-set X then, for n>=6, a(n-4) is the number 
               of (n-5)-subsets of X having exactly two elements in common with 
               Y. - Milan R. Janjic (agnus(AT)blic.net), Dec 28 2007
%C A007531 Convolution of A005843 with A008585. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Mar 07 2009]
%C A007531 a(n) = A000578(n) - A000567(n). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Sep 18 2009]
%D A007531 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A007531 R. K. Guy, Unsolved Problems in Theory of Numbers, Section D25.
%D A007531 L. B. W. Jolley, "Summation of Series", Dover Publications, 1961, p. 
               40.
%H A007531 <a href="Sindx_Tu.html#2wis">Index entries for two-way infinite sequences</
               a>
%H A007531 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%H A007531 Milan Janjic, <a href="http://www.pmfbl.org/janjic/">Enumerative Formulas 
               for Some Functions on Finite Sets</a>
%F A007531 Sum(Polygorial(3, i), i=1..n) - Daniel Dockery (peritus(AT)gmail.com) 
               Jun 16, 2003
%F A007531 a(0) = a(1) = a(2) = 0, a(n) = 3a(n-1) - 3a(n-2) + a(n-3) + 6. - Zak 
               Seidov, (zakseidov(AT)yahoo.com) Feb 09 2006.
%F A007531 G.f.: 6x^2/(1-x)^4. a(-n)=-a(n+2).
%F A007531 1/6 + 3/24 + 5/60 +...= 3/4 - Gary W. Adamson (qntmpkt(AT)yahoo.com), 
               Dec 21 2006
%F A007531 a(n)=numbperm(n,3). - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Apr 26 2007
%F A007531 Other than the first two 0's this sequence is the same as the sequence 
               a(n)=n^3-n. - Mohammad K. Azarian (azarian(AT)evansville.edu), Jul 
               26 2007
%F A007531 E.g.f.:x^3*exp(x) [From Geoffrey Critzer (critzer(AT)usd443.org), Feb 
               08 2009]
%p A007531 [seq(6*binomial(n,3),n=0..41)]; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Nov 24 2006
%p A007531 a:=n->sum(numbperm (n,2), j=0..n): seq(a(n), n=0..40); - Zerinvary Lajos 
               (zerinvarylajos(AT)yahoo.com), Apr 25 2007
%p A007531 seq(numbperm(n,3),n=0..41); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Apr 26 2007
%p A007531 a:=n->sum(sum(sum(1, j=0..n), k=1..n),m=2..n): seq(a(n), n=-1..40); - 
               Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 18 2007
%p A007531 seq(sum(n^2-1, k=1..n), n=-1..39); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Jan 28 2008
%p A007531 restart: G(x):=x^3*exp(x): f[0]:=G(x): for n from 1 to 41 do f[n]:=diff(f[n-1],
               x) od: x:=0: seq(f[n],n=0..41);# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Apr 05 2009]
%t A007531 Table[n^3 - 3n^2 + 2n, {n, 0, 41}]
%o A007531 (PARI) a(n)=n*(n-1)*(n-2)
%Y A007531 Cf. A002378.
%Y A007531 Equals 6*A000292(n-1). Cf. A002378, A005563, A084939, A084940, A084941, 
               A084942, A084943, A084944.
%Y A007531 Cf. A007531.
%Y A007531 Sequence in context: A086768 A160944 A160936 this_sequence A130669 A101854 
               A101877
%Y A007531 Adjacent sequences: A007528 A007529 A007530 this_sequence A007532 A007533 
               A007534
%K A007531 nonn,easy
%O A007531 0,4
%A A007531 N. J. A. Sloane (njas(AT)research.att.com), Robert G. Wilson v (rgwv(AT)rgwv.com)