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 A131404 #18 Sep 22 2024 02:02:16 %S A131404 1,1,1,1,5,1,1,7,7,1,1,11,13,11,1,1,13,27,27,13,1,1,17,39,65,39,17,1, %T A131404 1,19,61,111,111,61,19,1,1,23,79,193,221,193,79,23,1,1,25,109,283,433, %U A131404 433,283,109,25,1,1,29,133,425,715,925,715,425,133,29,1 %N A131404 a(n) = 2*A131402(n) - 1. %C A131404 Row sums = A131405: (1, 2, 7, 16, 37, 82, 179, ...). %H A131404 Andrew Howroyd, <a href="/A131404/b131404.txt">Table of n, a(n) for n = 0..1274</a> %F A131404 T(n,k) = 4*binomial(n, k) + 1 - 2*binomial(floor((n + k)/2), k) - 2*binomial(n-floor((k+1)/2), floor(k/2)). - _Andrew Howroyd_, Aug 09 2018 %e A131404 First few rows of the triangle are: %e A131404 1; %e A131404 1, 1; %e A131404 1, 5, 1; %e A131404 1, 7, 7, 1; %e A131404 1, 11, 13, 11, 1; %e A131404 1, 13, 27, 27, 13, 1; %e A131404 1, 17, 39, 65, 39, 17, 1; %e A131404 ... %o A131404 (PARI) T(n,k) = if(k <= n, 4*binomial(n,k) + 1 - 2*binomial((n + k)\2, k) - 2*binomial(n-(k+1)\2, k\2), 0) \\ _Andrew Howroyd_, Aug 09 2018 %o A131404 (Magma) /* As triangle */ [[4*Binomial(n, k) + 1 - 2*Binomial(Floor(n + k) div 2, k) - 2*Binomial(n-Floor((k+1)/2), Floor(k/2)): k in [0..n]]: n in [0.. 15]]; // _Vincenzo Librandi_, Aug 10 2018 %Y A131404 Row sums are A131405. %Y A131404 Cf. A131402. %K A131404 nonn,tabl,easy %O A131404 0,5 %A A131404 _Gary W. Adamson_, Jul 07 2007 %E A131404 Terms a(55) and beyond from _Andrew Howroyd_, Aug 09 2018