A132787 - OEIS

%I #6 Aug 10 2018 17:37:56

%S 1,1,1,1,5,1,1,11,11,1,1,19,39,19,1,1,29,99,99,29,1,1,41,209,349,209,

%T 41,1,1,55,391,979,979,391,55,1,1,71,671,2351,3527,2351,671,71,1,1,89,

%U 1079,5039,10583,10583,5039,1079,89,1,1,109,1649,9899,27719,38807,27719,9899,1649,109,1

%N Triangle read by rows: T(n,k) = 2*A001263(n,k) - 1.

%H Andrew Howroyd, <a href="/A132787/b132787.txt">Table of n, a(n) for n = 1..1275</a> (rows 1..50)

%F Equals 2*A001263 - A000012 as infinite lower triangular matrices; where A001263 = the Narayana triangle.

%F T(n,k) = 2*binomial(n-1, k-1) * binomial(n, k-1) / k - 1. - _Andrew Howroyd_, Aug 10 2018

%e First few rows of the triangle are:

%e   1;

%e   1, 1;

%e   1, 5, 1;

%e   1, 11, 11, 1;

%e   1, 19, 39, 19, 1;

%e   1, 29, 99, 99, 29, 1;

%e   ...

%o (PARI) T(n,k) = if(k<=n, 2*binomial(n-1, k-1) * binomial(n, k-1) / k - 1, 0); \\ _Andrew Howroyd_, Aug 10 2018

%Y Column 2 is A018387.

%Y Row sums are A132788.

%Y Cf. A001263.

%K nonn,tabl

%O 1,5

%A _Gary W. Adamson_, Aug 30 2007

%E a(20) corrected and terms a(56) and beyond from _Andrew Howroyd_, Aug 10 2018