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 A081205 #10 Sep 08 2022 08:45:09
%S A081205 1,3,10,20,70,126,462,792,3003,5005,19448,31824,125970,203490,817190,
%T A081205 1307504,5311735,8436285,34597290,54627300,225792840,354817320,
%U A081205 1476337800,2310789600,9669554100,15084504396,63432274896,98672427616
%N A081205 Staircase on Pascal's triangle.
%C A081205 Arrange Pascal's triangle as a square array. A081204 is then a diagonal staircase on the square array. The steps are (1,3),(10,20),(70,126),(462,792),....
%H A081205 Vincenzo Librandi, <a href="/A081205/b081205.txt">Table of n, a(n) for n = 0..200</a>
%F A081205 a(n) = binomial(ceiling((n+1)/2)+(n+1), n).
%F A081205 Conjecture: 4*n*(n-1)*(n+4)*(6*n^2-9*n-1)*a(n) +6*(n-1)*(27*n^2+29*n+4)*a(n-1) -3*n*(3*n-1)*(3*n+1)*(6*n^2+3*n-4)*a(n-2)=0. - _R. J. Mathar_, Nov 19 2014
%t A081205 Table[Binomial[Ceiling[(n+1)/2] + (n + 1), n], {n, 0, 30}] (* _Vincenzo Librandi_, Aug 07 2013 *)
%o A081205 (Magma) [Binomial(Ceiling((n+1)/2)+(n+1), n): n in [0..30]]; // _Vincenzo Librandi_ Aug 07 2013
%Y A081205 Cf. A065942, A081181, A081204.
%K A081205 easy,nonn
%O A081205 0,2
%A A081205 _Paul Barry_, Mar 11 2003