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 A185874 #26 Jul 20 2017 02:20:00
%S A185874 1,3,4,6,11,10,10,21,26,20,15,34,48,50,35,21,50,76,90,85,56,28,69,110,
%T A185874 140,150,133,84,36,91,150,200,230,231,196,120,45,116,196,270,325,350,
%U A185874 336,276,165,55,144,248,350,435,490,504,468,375,220,66,175,306,440,560,651,700,696,630,495,286,78,209,370,540,700,833,924,960,930,825,638,364,91,246,440,650,855,1036,1176,1260,1275,1210,1056,806,455,105,286,516,770,1025,1260,1456,1596,1665,1650,1540,1326,1001,560
%N A185874 Second accumulation array of A051340, by antidiagonals.
%C A185874 A member of the accumulation chain: A051340 < A141419 < A185874 < A185875 < A185876 < ... (See A144112 for the definition of accumulation array.)
%H A185874 G. C. Greubel, <a href="/A185874/b185874.txt">Table of n, a(n) for the first 50 rows, flattened</a>
%H A185874 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 A185874 T(n,k) = k*n*(n+1)*(2*n+3*k+1)/12 for k>=1, n>=1.
%e A185874 Northwest corner:
%e A185874 . 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...
%e A185874 . 4, 11, 21, 34, 50, 69, 91, 116, 144, 175, ...
%e A185874 . 10, 26, 48, 76, 110, 150, 196, 248, 306, 370, ...
%e A185874 . 20, 50, 90, 140, 200, 270, 350, 440, 540, 650, ...
%e A185874 . 35, 85, 150, 230, 325, 435, 560, 700, 855, 1025, ...
%e A185874 . 56, 133, 231, 350, 490, 651, 833, 1036, 1260, 1505, ...
%e A185874 . 84, 196, 336, 504, 700, 924, 1176, 1456, 1764, 2100, ...
%e A185874 . 120, 276, 468, 696, 960, 1260, 1596, 1968, 2376, 2820, ...
%e A185874 . 165, 375, 630, 930, 1275, 1665, 2100, 2580, 3105, 3675, ...
%e A185874 . 220, 495, 825, 1210, 1650, 2145, 2695, 3300, 3960, 4675, ...
%e A185874 ...
%t A185874 f[n_, k_] := (1/12)*k*n*(1 + n)*(1 + 3*k + 2*n);
%t A185874 TableForm[Table[f[n, k], {n, 1, 10}, {k, 1, 15}]]
%t A185874 Table[f[n - k + 1, k], {n, 14}, {k, n, 1, -1}] // Flatten
%Y A185874 Cf. A144112, A051340, A141419, A185875, A185876.
%Y A185874 Row 1 to 5: A000217, A115056, 2*A140096, 10*A000096, 5*A059845.
%Y A185874 Column 1 to 3: A000292, A051925, A267370 and 3*A005581.
%Y A185874 Main diagonal: A117066.
%K A185874 nonn,tabl,easy
%O A185874 1,2
%A A185874 _Clark Kimberling_, Feb 05 2011
%E A185874 Edited by _Bruno Berselli_, Jan 14 2016