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A130812 If X_1,...,X_n is a partition of a 2n-set X into 2-blocks then a(n) is equal to the number of 6-subsets of X containing none of X_i, (i=1,...n). 3

%I

%S 64,448,1792,5376,13440,29568,59136,109824,192192,320320,512512,

%T 792064,1188096,1736448,2480640,3472896,4775232,6460608,8614144,

%U 11334400,14734720,18944640,24111360,30401280,38001600,47121984,57996288,70884352,86073856,103882240

%N If X_1,...,X_n is a partition of a 2n-set X into 2-blocks then a(n) is equal to the number of 6-subsets of X containing none of X_i, (i=1,...n).

%C Number of n permutations (n>=6) of 3 objects u,v,z, with repetition allowed, containing n-6 u's. Example: if n=6 then n-6 =(0) zero u, a(1)=64. - _Zerinvary Lajos_, Aug 05 2008

%C a(n) is the number of 5-dimensional elements in an n-cross polytope where n>=6. - _Patrick J. McNab_, Jul 06 2015

%H Vincenzo Librandi, <a href="/A130812/b130812.txt">Table of n, a(n) for n = 6..1000</a>

%H Milan Janjic, <a href="http://www.pmfbl.org/janjic/">Two Enumerative Functions</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CrossPolytope.html">Cross Polytope</a>

%F a(n) = binomial(2*n,6) + binomial(n,2)*binomial(2*n-4,2) - n*binomial(2*n-2,4) - binomial(n,3).

%F a(n) = C(n,n-6)*2^6, n>=6. - _Zerinvary Lajos_, Dec 07 2007

%F G.f.: 64*x^6/(1-x)^7. - _Colin Barker_, Mar 20 2012

%p a:=n->binomial(2*n,6)+binomial(n,2)*binomial(2*n-4,2)-n*binomial(2*n-2,4)-binomial(n,3);

%p seq(binomial(n,n-6)*2^6,n=6..32); # _Zerinvary Lajos_, Dec 07 2007

%p seq(binomial(n+5, 6)*2^6, n=1..22); # _Zerinvary Lajos_, Aug 05 2008

%t CoefficientList[Series[64/(1-x)^7,{x,0,30}],x] (* _Vincenzo Librandi_, Mar 21 2012 *)

%o (MAGMA) [Binomial(2*n,6)+Binomial(n,2)*Binomial(2*n-4,2)- n*Binomial(2*n-2,4)-Binomial(n,3): n in [6..40]]; // _Vincenzo Librandi_, Jul 09 2015

%Y Cf. A038207, A000079, A001787, A001788, A001789, A003472, A054849, A002409, A054851, A140325, A140354, A046092, A130809, A130810, A130811. - _Zerinvary Lajos_, Aug 05 2008

%K nonn,easy

%O 6,1

%A _Milan Janjic_, Jul 16 2007

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Last modified July 31 04:50 EDT 2021. Contains 346367 sequences. (Running on oeis4.)