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A157635 Triangle read by rows: T(n,m) = 1 if n*m*(n-m) = 0, and n*m*(n-m) otherwise.

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