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%I #16 Jul 20 2017 02:19:40
%S 1,4,5,10,19,15,20,46,55,35,35,90,130,125,70,56,155,250,290,245,126,
%T 84,245,425,550,560,434,210,120,364,665,925,1050,980,714,330,165,516,
%U 980,1435,1750,1820,1596,1110,495,220,705,1380,2100,2695,3010,2940,2460,1650,715,286,935,1875,2940,3920,4606,4830,4500,3630,2365,1001,364,1210,2475,3975,5460,6664,7350,7350,6600,5170
%N Third accumulation array of A051340, by antidiagonals.
%C A member of the accumulation chain A051340 < A141419 < A185874 < A185875 < A185876 < ... (See A144112 for the definition of accumulation array.)
%H G. C. Greubel, <a href="/A185875/b185875.txt">Table of n, a(n) for the first 50 rows, flattened</a>
%H Johann Cigler, <a href="https://arxiv.org/abs/1611.05252">Some elementary observations on Narayana polynomials and related topics</a>, arXiv:1611.05252 [math.CO], 2016. See p. 24.
%F T(n,k) = (3*n+4*k+5)*C(k,2)*C(n,3)/12, k>=1, n>=1.
%e Northwest corner:
%e 1, 4, 10, 20, 35
%e 5, 19, 46, 90, 155
%e 15, 55, 130, 250, 425
%e 35, 125, 290, 550, 925
%t f[n_,k_]:= k*(1+k)*n*(1+n)*(2+n)*(5+4*k+3*n)/144;
%t TableForm[Table[f[n,k],{n,1,10},{k,1,15}]]
%t Table[f[n-k+1,k],{n,14},{k,n,1,-1}]//Flatten
%Y Cf. A051340, A141419, A144112, A185875, A185876.
%Y Row 1: A000292; Column 1: A000332.
%K nonn,tabl
%O 1,2
%A _Clark Kimberling_, Feb 05 2011
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