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 A052516 #44 Sep 08 2022 08:44:59
%S A052516 0,0,0,0,0,0,20,70,182,420,912,1914,3938,8008,16172,32526,65262,
%T A052516 130764,261800,523906,1048154,2096688,4193796,8388054,16776614,
%U A052516 33553780,67108160,134216970
%N A052516 Number of pairs of sets of cardinality at least 3.
%C A052516 The number of functions f:[n]->[2] such that f maps at least 3 elements to 1 and at least 3 elements to 2. a(6) = 20 since there are C(6,3) ways to choose the 3 elements of {1,2,3,4,5,6} that f maps to 1. - _Dennis P. Walsh_, Dec 09 2014
%H A052516 Vincenzo Librandi, <a href="/A052516/b052516.txt">Table of n, a(n) for n = 0..2000</a>
%H A052516 INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=82">Encyclopedia of Combinatorial Structures 82</a>
%H A052516 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (5,-9,7,-2).
%F A052516 E.g.f.: (exp(x) -1)^2 -x*(2+x)*exp(x) +2*x +2*x^2 +x^3 +x^4/4.
%F A052516 (n-1)*a(n+2) + (1-3*n)*a(n+1) + 2*(n+1)*a(n) = 0, a(0) = .. a(5) = 0, a(6) = 20.
%F A052516 G.f.: 2*x^6*(10-15*x+6*x^2)/((1-x)^3*(1-2*x)). - _Colin Barker_, Feb 19 2012
%F A052516 a(n) = max(0,2^n-n^2-n-2). - _Dennis P. Walsh_, Dec 09 2014
%F A052516 E.g.f.: (exp(x) - 1 - x - x^2/2)^2. - _Dennis P. Walsh_, Dec 09 2014
%p A052516 Pairs spec := [S,{S=Prod(B,B),B=Set(Z,3 <= card)},labeled]: seq(combstruct[count](spec,size=n), n=0..20);
%p A052516 with (combstruct):ZL:=[S,{S=Sequence(U,card=r),U=Set(Z,card>=3)}, labeled]: seq(count(subs(r=2,ZL),size=m),m=0..20); # _Zerinvary Lajos_, Mar 09 2007
%p A052516 seq(max(0,2^n-n^2-n-2), n=0..40); # _Dennis P. Walsh_, Dec 09 2014
%t A052516 Table[Max[0,2^n-n^2-n-2],{n,0,30}] (* _Vladimir Joseph Stephan Orlovsky_, Feb 15 2011*)
%o A052516 (PARI) a(n)=max(0,2^n-n^2-n-2) \\ _Charles R Greathouse IV_, Nov 20 2011
%o A052516 (Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( (Exp(x) -1-x-x^2/2)^2 )); [0,0,0,0,0] cat [Factorial(n+5)*b[n]: n in [1..m-6]]; // _G. C. Greubel_, May 13 2019
%o A052516 (Sage) (2*x^6*(10-15*x+6*x^2)/((1-x)^3*(1-2*x))).series(x, 30).coefficients(x, sparse=False) # _G. C. Greubel_, May 13 2019
%Y A052516 Cf. A052515.
%K A052516 easy,nonn
%O A052516 0,7
%A A052516 encyclopedia(AT)pommard.inria.fr, Jan 25 2000