%I #25 Sep 08 2022 08:45:01
%S 4,120,1140,6545,27720,95284,280840,735130,1750540,3858140,7971964,
%T 15596035,29112720,52174360,90223760,151173044,246274580,391222160,
%U 607525380,924205205,1379864024,2025189100,2925954200,4166590350
%N Number of labeled pure 2-complexes on n nodes with 3 2-simplexes.
%H Vincenzo Librandi, <a href="/A054644/b054644.txt">Table of n, a(n) for n = 4..1000</a>
%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (10,-45,120,-210,252,-210,120,-45,10,-1).
%F a(n) = binomial(binomial(n, 3), 3) = 4*binomial(n, 4) + 100*binomial(n, 5) + 480*binomial(n, 6) + 945*binomial(n, 7) + 840*binomial(n, 8) + 280*binomial(n, 9) = n*(n-1)*(n-2)*(n-3)*(n^2+2)*(n^3 - 3*n^2 + 2*n - 12)/1296.
%F G.f.: x^4*(4 + 80*x + 120*x^2 + 65*x^3 + 10*x^4 + x^5)/(1-x)^10. - _Colin Barker_, Jan 19 2012
%t Table[Binomial[Binomial[n,3],3],{n,4,60}] (* _Vladimir Joseph Stephan Orlovsky_, May 30 2010 *)
%t LinearRecurrence[{10,-45,120,-210,252,-210,120,-45,10,-1},{4,120,1140,6545,27720,95284,280840,735130,1750540,3858140},30] (* _Vincenzo Librandi_, Apr 30 2012 *)
%o (Sage) [(binomial(binomial(n,3),3)) for n in range(4, 28)] # _Zerinvary Lajos_, Nov 30 2009
%o (Magma) [n*(n-1)*(n-2)*(n-3)*(n^2+2)*(n^3-3*n^2+2*n-12)/1296: n in [4..30]]; // _Vincenzo Librandi_, Apr 30 2012
%Y Cf. A054563.
%K nonn,easy
%O 4,1
%A _Vladeta Jovovic_, Apr 15 2000
%E More terms from _James A. Sellers_, Apr 16 2000
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