This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A054644 #26 Jul 02 2025 16:01:59
%S A054644 4,120,1140,6545,27720,95284,280840,735130,1750540,3858140,7971964,
%T A054644 15596035,29112720,52174360,90223760,151173044,246274580,391222160,
%U A054644 607525380,924205205,1379864024,2025189100,2925954200,4166590350
%N A054644 Number of labeled pure 2-complexes on n nodes with 3 2-simplexes.
%H A054644 Vincenzo Librandi, <a href="/A054644/b054644.txt">Table of n, a(n) for n = 4..1000</a>
%H A054644 <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 A054644 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 A054644 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 A054644 Table[Binomial[Binomial[n,3],3],{n,4,60}] (* _Vladimir Joseph Stephan Orlovsky_, May 30 2010 *)
%t A054644 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 A054644 (Sage) [(binomial(binomial(n,3),3)) for n in range(4, 28)] # _Zerinvary Lajos_, Nov 30 2009
%o A054644 (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 A054644 Cf. A054563.
%K A054644 nonn,easy
%O A054644 4,1
%A A054644 _Vladeta Jovovic_, Apr 15 2000
%E A054644 More terms from _James Sellers_, Apr 16 2000