%I #16 Nov 04 2018 03:57:59
%S 1,3,1,6,16,1,10,100,50,1,15,400,750,120,1,21,1225,6125,3675,245,1,28,
%T 3136,34300,54880,13720,448,1,36,7056,148176,518616,345744,42336,756,
%U 1,45,14400,529200,3556224,5186160,1693440,113400,1200,1,55,27225,1633500
%N If (a_n) is a sequence then let L(a_n)=(b_n) where b_n = a_n^2 - a_{n-1} a_{n+1}. The given sequence is the rows of the triangle obtained by computing L^2(binomial(n,k)).
%C L(binomial(n,k)) gives the Narayana numbers, A001263.
%H Peter R. W. McNamara and Bruce E. Sagan, <a href="http://arxiv.org/abs/0808.1065">Infinite log-concavity: developments and conjectures</a>, arXiv:0808.1065 [math.CO], 2008-2009.
%H Peter R. W. McNamara and Bruce E. Sagan, <a href="https://doi.org/10.1016/j.aam.2009.03.001">Infinite log-concavity: developments and conjectures</a>, Advances in Applied Mathematics, 44 (1) (2010), 1-15.
%F a(n,k) = binomial(n,k)^2 * binomial(n,k-1) * binomial(n,k-2) / (n*binomial(n,2)).
%t a[n_, k_] := 2 * Binomial[n, k]^2 * Binomial[n, k - 1] * Binomial[n, k - 2] / ((n - 1) n^2); Table[ a[n, k], {n, 2, 11}, {k, 2, n}] // Flatten (* _Robert G. Wilson v_, Aug 03 2008 *)
%Y Cf. A001263.
%K nonn,tabl
%O 3,2
%A _Bruce E. Sagan_, Jul 28 2008
%E More terms from _Robert G. Wilson v_, Aug 03 2008