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%I #14 Sep 08 2022 08:45:31
%S 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 1,19,61,111,111,61,19,1,1,23,79,193,221,193,79,23,1,1,25,109,283,433,
%U 433,283,109,25,1,1,29,133,425,715,925,715,425,133,29,1
%N a(n) = 2*A131402(n) - 1.
%C Row sums = A131405: (1, 2, 7, 16, 37, 82, 179, ...).
%H Andrew Howroyd, <a href="/A131404/b131404.txt">Table of n, a(n) for n = 0..1274</a>
%F 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 First few rows of the triangle are:
%e 1;
%e 1, 1;
%e 1, 5, 1;
%e 1, 7, 7, 1;
%e 1, 11, 13, 11, 1;
%e 1, 13, 27, 27, 13, 1;
%e 1, 17, 39, 65, 39, 17, 1;
%e ...
%o (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 (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 Row sums are A131405.
%Y Cf. A131402.
%K nonn,tabl
%O 0,5
%A _Gary W. Adamson_, Jul 07 2007
%E Terms a(55) and beyond from _Andrew Howroyd_, Aug 09 2018
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