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%I #7 Sep 08 2022 08:45:42
%S 1,1,1,1,2,1,1,6,6,1,1,12,16,12,1,1,20,30,30,20,1,1,30,48,54,48,30,1,
%T 1,42,70,84,84,70,42,1,1,56,96,120,128,120,96,56,1,1,72,126,162,180,
%U 180,162,126,72,1,1,90,160,210,240,250,240,210,160,90,1
%N Triangle read by rows: T(n,m) = 1 if n*m*(n-m) = 0, and n*m*(n-m) otherwise.
%C Row sums are: {1, 2, 4, 14, 42, 102, 212, 394, 674, 1082, 1652, ...}.
%H G. C. Greubel, <a href="/A157635/b157635.txt">Rows n = 0..100 of triangle, flattened</a>
%F T(n,m) = 1 if n*m*(n - m) = 0, and n*m*(n - m) otherwise.
%e Triangle begins as:
%e 1;
%e 1, 1;
%e 1, 2, 1;
%e 1, 6, 6, 1;
%e 1, 12, 16, 12, 1;
%e 1, 20, 30, 30, 20, 1;
%e 1, 30, 48, 54, 48, 30, 1;
%t Table[If[n*m*(n-m)==0, 1, n*m*(n-m)], {n, 0, 10}, {m, 0, n}]//Flatten (* modified by _G. C. Greubel_, Apr 09 2019 *)
%o (PARI) {T(n,k) = if(n*k*(n-k)==0, 1, n*k*(n-k))}; \\ _G. C. Greubel_, Apr 09 2019
%o (Magma) [[n*k*(n-k) eq 0 select 1 else n*k*(n-k): k in [0..n]]: n in [0..10]]; // _G. C. Greubel_, Apr 09 2019
%o (Sage)
%o @CachedFunction
%o def T(n, k):
%o if (n*k*(n-k)==0): return 1
%o else: return n*k*(n-k)
%o [[T(n, k) for k in (0..n)] for n in (0..10)] # _G. C. Greubel_, Apr 09 2019
%K nonn,tabl
%O 0,5
%A _Roger L. Bagula_, Mar 03 2009
%E Edited by _G. C. Greubel_, Apr 09 2019
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