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 A081204 #17 Sep 08 2022 08:45:09
%S A081204 1,2,3,10,15,56,84,330,495,2002,3003,12376,18564,77520,116280,490314,
%T A081204 735471,3124550,4686825,20030010,30045015,129024480,193536720,
%U A081204 834451800,1251677700,5414950296,8122425444,35240152720,52860229080,229911617056
%N A081204 Staircase on Pascal's triangle.
%C A081204 Arrange Pascal's triangle as a square array. This sequence is then a diagonal staircase on the square array.
%H A081204 Vincenzo Librandi, <a href="/A081204/b081204.txt">Table of n, a(n) for n = 0..200</a>
%F A081204 a(n) = binomial(ceiling((n)/2) + n, n).
%F A081204 a(n) = Sum_{k=0..floor(n/2)} binomial(n+k-1, k). - _Paul Barry_, Jul 06 2004
%F A081204 Conjecture: 4*n*(n+1)*(6*n^2 - 15*n + 8)*a(n) + 6*n*(9*n-7)*a(n-1) - 3*(3*n-4)*(3*n-2)*(6*n^2-3*n-1)*a(n-2) = 0. - _R. J. Mathar_, Nov 07 2014
%F A081204 Conjecture: 8*n^2*(n+1)*a(n) - 12*n*(83*n^2 - 313*n + 232)*a(n-1) + 6*(-9*n^3 - 377*n + 384)*a(n-2) + 9*(3*n-5)*(83*n-64)*(3*n-7)*a(n-3) = 0. - _R. J. Mathar_, Nov 07 2014
%t A081204 Table[Binomial[Ceiling[(n)/2] + n, n], {n, 0, 30}] (* _Vincenzo Librandi_, Aug 07 2013 *)
%o A081204 (Magma) [Binomial(Ceiling((n)/2) + n, n): n in [0..30]]; // _Vincenzo Librandi_, Aug 07 2013
%Y A081204 Cf. A065942, A081181, A081205.
%K A081204 easy,nonn
%O A081204 0,2
%A A081204 _Paul Barry_, Mar 11 2003