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A141432 Triangle T(n,k) = (k+1)*(n-k-1) read by rows.

%I A141432 #16 Apr 01 2021 17:27:06
%S A141432 -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,
%T A141432 12,15,16,15,12,7,0,-9,14,18,20,20,18,14,8,0,-10,16,21,24,25,24,21,16,
%U A141432 9,0,-11
%N A141432 Triangle T(n,k) = (k+1)*(n-k-1) read by rows.
%H A141432 G. C. Greubel, <a href="/A141432/b141432.txt">Rows n = 1..50 of the triangle, flattened</a>
%F A141432 T(n,k) = (k+1)*(n-k-1).
%F A141432 Sum_{k=1..n} T(n, k) = n*(n^2 - 13)/6.
%F A141432 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
%e A141432 Triangle begins as:
%e A141432   -2;
%e A141432    0, -3;
%e A141432    2,  0, -4;
%e A141432    4,  3,  0, -5;
%e A141432    6,  6,  4,  0, -6;
%e A141432    8,  9,  8,  5,  0, -7;
%e A141432   10, 12, 12, 10,  6,  0, -8;
%e A141432   12, 15, 16, 15, 12,  7,  0, -9;
%e A141432   14, 18, 20, 20, 18, 14,  8,  0, -10;
%e A141432   16, 21, 24, 25, 24, 21, 16,  9,   0, -11;
%p A141432 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
%t A141432 Table[(k+1)*(n-k-1), {n, 12}, {k, n}]//Flatten (* modified by _G. C. Greubel_, Apr 01 2021 *)
%o A141432 (Magma) [(k+1)*(n-k-1): k in [1..n], n in [1..12]]; // _G. C. Greubel_, Apr 01 2021
%o A141432 (Sage) flatten([[(k+1)*(n-k-1) for k in (1..n)] for n in (1..12)]) # _G. C. Greubel_, Apr 01 2021
%Y A141432 Cf. A003991, A004247.
%K A141432 tabl,easy,sign
%O A141432 1,1
%A A141432 _Roger L. Bagula_ and _Gary W. Adamson_, Aug 06 2008