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 A244864 #24 Oct 21 2022 21:39:05
%S A244864 1,10,49,165,440,1001,2030,3774,6555,10780,16951,25675,37674,53795,
%T A244864 75020,102476,137445,181374,235885,302785,384076,481965,598874,737450,
%U A244864 900575,1091376,1313235,1569799,1864990,2203015,2588376,3025880,3520649,4078130,4704105,5404701,6186400,7056049
%N A244864 a(n) = binomial(n+5,5) + 4*binomial(n+4,5) + 4*binomial(n+3,5) + binomial(n+2,5).
%H A244864 Alois P. Heinz, <a href="/A244864/b244864.txt">Table of n, a(n) for n = 0..1000</a>
%H A244864 R. P. Stanley, <a href="/A002721/a002721.pdf">Examples of Magic Labelings</a>, Unpublished Notes, 1973 [Cached copy, with permission]
%H A244864 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).
%F A244864 G.f.: (x+1)*(x^2+3*x+1)/(x-1)^6; a(n) = (2*n+3)*(n+2)*(n+1)*(n^2+3*n+4)/24. - _Alois P. Heinz_, Jul 11 2014
%F A244864 a(n) = Sum_{k=A000292(n)..A000292(n+1)} k. - _J. M. Bergot_, Feb 25 2015
%p A244864 a:= n-> (2*n+3)*(n+2)*(n+1)*(n^2+3*n+4)/24:
%p A244864 seq(a(n), n=0..40); # _Alois P. Heinz_, Jul 11 2014
%t A244864 Table[Binomial[n+5,5]+4*Binomial[n+4,5]+4*Binomial[n+3,5]+ Binomial[ n+2,5],{n,0,40}] (* or *) LinearRecurrence[{6,-15,20,-15,6,-1},{1,10,49,165,440,1001},40] (* _Harvey P. Dale_, Nov 13 2014 *)
%t A244864 a[n_] := (2 n^5 + 15 n^4 + 48 n^3 + 81 n^2 + 70 n + 24)/ 24; Array[a, 40, 0] (* or *)
%t A244864 CoefficientList[Series[(x^3 + 4 x^2 + 4 x + 1)/(x - 1)^6, {x, 0, 40}], x] (* _Robert G. Wilson v_, Feb 26 2015 *)
%o A244864 (PARI) a(n)=(2*n+3)*(n+2)*(n+1)*(n^2+3*n+4)/24 \\ _Charles R Greathouse IV_, Oct 21 2022
%K A244864 nonn,easy
%O A244864 0,2
%A A244864 _N. J. A. Sloane_, Jul 07 2014