OFFSET
1,1
LINKS
G. C. Greubel, Rows n = 1..50 of the triangle, flattened
FORMULA
T(n,k) = (k+1)*(n-k-1).
Sum_{k=1..n} T(n, k) = n*(n^2 - 13)/6.
G.f.: Sum_{n>=0} Sum_{k>=0} T(n,k)*x^n*y^k = (2*x-1-y)/((1-y)^3*(x-1)^2). - R. J. Mathar, Feb 19 2020
EXAMPLE
Triangle begins as:
-2;
0, -3;
2, 0, -4;
4, 3, 0, -5;
6, 6, 4, 0, -6;
8, 9, 8, 5, 0, -7;
10, 12, 12, 10, 6, 0, -8;
12, 15, 16, 15, 12, 7, 0, -9;
14, 18, 20, 20, 18, 14, 8, 0, -10;
16, 21, 24, 25, 24, 21, 16, 9, 0, -11;
MAPLE
A141432:= (n, k) -> (k+1)*(n-k-1); seq(seq(A141432(n, k), k=1..n), n=1..12); # G. C. Greubel, Apr 01 2021
MATHEMATICA
Table[(k+1)*(n-k-1), {n, 12}, {k, n}]//Flatten (* modified by G. C. Greubel, Apr 01 2021 *)
PROG
(Magma) [(k+1)*(n-k-1): k in [1..n], n in [1..12]]; // G. C. Greubel, Apr 01 2021
(Sage) flatten([[(k+1)*(n-k-1) for k in (1..n)] for n in (1..12)]) # G. C. Greubel, Apr 01 2021
CROSSREFS
KEYWORD
AUTHOR
Roger L. Bagula and Gary W. Adamson, Aug 06 2008
STATUS
approved