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 A053310 #29 Sep 08 2022 08:45:00
%S A053310 1,12,75,330,1155,3432,9009,21450,47190,97240,189618,352716,629850,
%T A053310 1085280,1812030,2941884,4657983,7210500,10935925,16280550,23828805,
%U A053310 34337160,48774375,68368950,94664700,129585456,175509972,235358200
%N A053310 a(n) = (n+3)*binomial(n+8, 8)/3.
%C A053310 If Y is a 3-subset of an n-set X then, for n>=11, a(n-11) is the number of 11-subsets of X having at least two elements in common with Y. - _Milan Janjic_, Nov 23 2007
%D A053310 A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 189, 194-196.
%H A053310 G. C. Greubel, <a href="/A053310/b053310.txt">Table of n, a(n) for n = 0..1000</a>
%H A053310 <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 A053310 G.f.: (1+2*x)/(1-x)^10.
%F A053310 a(n) = binomial(n+8,n+2)*binomial(n+3,n)/28. - _Zerinvary Lajos_, May 12 2006
%t A053310 CoefficientList[Series[(1+2*x)/(1-x)^10, {x, 0, 50}], x] (* _G. C. Greubel_, May 24 2018 *)
%t A053310 Table[(n+3) Binomial[n+8,8]/3,{n,0,30}] (* or *) LinearRecurrence[{10,-45,120,-210,252,-210,120,-45,10,-1},{1,12,75,330,1155,3432,9009,21450,47190,97240},30] (* _Harvey P. Dale_, Feb 25 2021 *)
%o A053310 (PARI) for(n=0, 30, print1((n+3)*binomial(n+8, 8)/3, ", ")) \\ _G. C. Greubel_, May 24 2018
%o A053310 (Magma) [(n+3)*Binomial(n+8, 8)/3: n in [0..30]]; // _G. C. Greubel_, May 24 2018
%Y A053310 Partial sums of A053367.
%Y A053310 Cf. A053367, A053347, A000581.
%Y A053310 Cf. A093560 ((3, 1) Pascal, column m=9).
%K A053310 easy,nonn
%O A053310 0,2
%A A053310 _Barry E. Williams_, Mar 06 2000