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 A054559 #34 Mar 08 2022 03:39:10
%S A054559 30,180,630,1680,3780,7560,13860,23760,38610,60060,90090,131040,
%T A054559 185640,257040,348840,465120,610470,790020,1009470,1275120,1593900,
%U A054559 1973400,2421900,2948400,3562650,4275180,5097330,6041280,7120080,8347680,9738960,11309760,13076910
%N A054559 Number of labeled pure 2-complexes on n nodes (0-simplexes) with 5 2-simplexes and 8 1-simplexes.
%C A054559 Number of {T_1,T_2,...,T_k} where T_i,i=1..k are 3-subsets of an n-set such that {D | D is 2-subset of T_i for some i=1..k} has l elements; k=5,l=8.
%C A054559 Let H be the n X n Hilbert matrix H(i,j) = 1/(i+j-1) for 1 <= i,j <= n. Let B be the inverse matrix of H. The sum of the elements in row 3 of B equals -a(n+2). - _T. D. Noe_, May 01 2011
%D A054559 V. Jovovic, On the number of two-dimensional simplicial complexes (in Russian), Metody i sistemy tekhnicheskoy diagnostiki, Vypusk 16, Mezhvuzovskiy zbornik nauchnykh trudov, Izdatelstvo Saratovskogo universiteta, 1991.
%H A054559 Vincenzo Librandi, <a href="/A054559/b054559.txt">Table of n, a(n) for n = 5..1000</a>
%H A054559 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).
%F A054559 a(n) = 30*C(n,5) = 30*A000389(n) = n*(n-1)*(n-2)*(n-3)*(n-4)/4.
%F A054559 G.f.: 30*x^5/(1-x)^6. - _Colin Barker_, Jan 19 2012
%F A054559 a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6). - _Vincenzo Librandi_, Apr 29 2012
%F A054559 E.g.f.: x^5*exp(x)/4. - _G. C. Greubel_, Nov 23 2017
%F A054559 From _Amiram Eldar_, Mar 08 2022: (Start)
%F A054559 Sum_{n>=5} 1/a(n) = 1/24.
%F A054559 Sum_{n>=5} (-1)^(n+1)/a(n) = 8*log(2)/3 - 131/72. (End)
%t A054559 Table[n*(n+1)*(n+2)*(n+3)*(n+4)/4, {n,1,100}] (* _Vladimir Joseph Stephan Orlovsky_, Jul 21 2009 *)
%t A054559 CoefficientList[Series[30/(1-x)^6,{x,0,30}],x] (* _Vincenzo Librandi_, Apr 29 2012 *)
%o A054559 (Magma) I:=[30, 180, 630, 1680, 3780, 7560]; [n le 6 select I[n] else 6*Self(n-1)-15*Self(n-2)+20*Self(n-3)-15*Self(n-4)+6*Self(n-5)-Self(n-6): n in [1..30]]; // _Vincenzo Librandi_, Apr 29 2012
%o A054559 (PARI) x='x+O('x^30); Vec(serlaplace(x^5*exp(x)/4)) \\ _G. C. Greubel_, Nov 23 2017
%Y A054559 Cf. A054557.
%Y A054559 Cf. A000389, A052787.
%K A054559 nonn,easy
%O A054559 5,1
%A A054559 _Vladeta Jovovic_, Apr 10 2000