OFFSET
1,2
COMMENTS
LINKS
G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened
Johann Cigler, Some elementary observations on Narayana polynomials and related topics, arXiv:1611.05252 [math.CO], 2016. See p. 24.
FORMULA
T(n,k) = k*n*(n+1)*(2*n+3*k+1)/12 for k>=1, n>=1.
EXAMPLE
Northwest corner:
. 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...
. 4, 11, 21, 34, 50, 69, 91, 116, 144, 175, ...
. 10, 26, 48, 76, 110, 150, 196, 248, 306, 370, ...
. 20, 50, 90, 140, 200, 270, 350, 440, 540, 650, ...
. 35, 85, 150, 230, 325, 435, 560, 700, 855, 1025, ...
. 56, 133, 231, 350, 490, 651, 833, 1036, 1260, 1505, ...
. 84, 196, 336, 504, 700, 924, 1176, 1456, 1764, 2100, ...
. 120, 276, 468, 696, 960, 1260, 1596, 1968, 2376, 2820, ...
. 165, 375, 630, 930, 1275, 1665, 2100, 2580, 3105, 3675, ...
. 220, 495, 825, 1210, 1650, 2145, 2695, 3300, 3960, 4675, ...
...
MATHEMATICA
f[n_, k_] := (1/12)*k*n*(1 + n)*(1 + 3*k + 2*n);
TableForm[Table[f[n, k], {n, 1, 10}, {k, 1, 15}]]
Table[f[n - k + 1, k], {n, 14}, {k, n, 1, -1}] // Flatten
CROSSREFS
Main diagonal: A117066.
KEYWORD
AUTHOR
Clark Kimberling, Feb 05 2011
EXTENSIONS
Edited by Bruno Berselli, Jan 14 2016
STATUS
approved