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 A051743 #22 Dec 21 2016 02:47:12
%S A051743 2,7,18,39,75,132,217,338,504,725,1012,1377,1833,2394,3075,3892,4862,
%T A051743 6003,7334,8875,10647,12672,14973,17574,20500,23777,27432,31493,35989,
%U A051743 40950,46407,52392,58938,66079,73850,82287,91427,101308,111969,123450
%N A051743 a(n) = (1/24)*n*(n + 5)*(n^2 + n + 6).
%C A051743 This is exactly the number of directed column-convex polyominoes. [Something is clearly missing from this sentence; as it stands, it makes no reference to the index n. - _Jon E. Schoenfield_, Dec 20 2016]
%C A051743 Let A be the Hessenberg n X n matrix defined by: A[1,j]=j mod 2, A[i,i]:=1, A[i,i-1]=-1, and A[i,j]=0 otherwise. Then, for n>=5, a(n-3)=coeff(charpoly(A,x),x^(n-4)). [_Milan Janjic_, Jan 24 2010]
%H A051743 Harvey P. Dale, <a href="/A051743/b051743.txt">Table of n, a(n) for n = 1..1000</a>
%H A051743 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5, -10, 10, -5, 1).
%F A051743 a(n) = binomial(n+3, n-1) + binomial(n, n-1) = binomial(n+3, 4) + binomial(n, 1), n > 0.
%F A051743 From _Harvey P. Dale_, Nov 29 2011: (Start)
%F A051743 a(1)=2, a(2)=7, a(3)=18, a(4)=39, a(5)=75, a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5).
%F A051743 G.f.: (x^3-3*x^2+3*x-2)/(x-1)^5. (End)
%F A051743 E.g.f.: (1/24)*(48*x + 36*x^2 + 12*x^3 + x^4)*exp(x). - _G. C. Greubel_, Dec 21 2016
%t A051743 Table[(n (n + 5) (n^2 + n + 6))/24, {n, 50}] (* or *) LinearRecurrence[ {5, -10, 10, -5, 1}, {2, 7, 18, 39, 75}, 50]
%o A051743 (PARI) Vec((x^3-3*x^2+3*x-2)/(x-1)^5 + O(x^50)) \\ _G. C. Greubel_, Dec 21 2016
%Y A051743 Cf. A005435, A006027, A105450.
%K A051743 nonn,easy
%O A051743 1,1
%A A051743 Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Dec 07 1999