%I #20 Sep 22 2024 11:05:21
%S 1,1,1,1,2,1,1,9,9,1,1,8,36,8,1,1,8,33,33,8,1,1,9,38,33,38,9,1,1,10,
%T 44,41,41,44,10,1,1,11,52,52,54,52,52,11,1,1,12,62,67,76,76,67,62,12,
%U 1,1,12,72,86,105,113,105,86,72,12,1,1,13,84,108,144,169,169,144,108,84,13,1
%N Triangle read by rows: T(n, k) = round(f(n)/(f(k)*f(n-k))), where f(n) = n!*binomial(n,2), f(0) = f(1) = 1.
%H G. C. Greubel, <a href="/A141601/b141601.txt">Rows n = 0..50 of the triangle, flattened</a>
%F T(n, k) = round( f(n)/(f(k)*f(n-k)) ), where f(n) = n*b(n)*f(n-1)/b(n-1), f(0) = f(1) = 1, b(n) = binomial(n, 2), b(0) = b(1) = 1.
%e Triangle begins as:
%e 1;
%e 1, 1;
%e 1, 2, 1;
%e 1, 9, 9, 1;
%e 1, 8, 36, 8, 1;
%e 1, 8, 33, 33, 8, 1;
%e 1, 9, 38, 33, 38, 9, 1;
%e 1, 10, 44, 41, 41, 44, 10, 1;
%e 1, 11, 52, 52, 54, 52, 52, 11, 1;
%e 1, 12, 62, 67, 76, 76, 67, 62, 12, 1;
%e 1, 12, 72, 86, 105, 113, 105, 86, 72, 12, 1;
%e ...
%t f[n_]:= If[n<2, 1, n!*Binomial[n, 2]];
%t T[n_, k_]:= Round[f[n]/(f[n-k]*f[k])];
%t Table[T[n,k], {n,0,14}, {k,0,n}]//Flatten
%o (Magma)
%o f:= func< n | n le 1 select 1 else Factorial(n)*Binomial(n,2) >;
%o A141601:= func< n,k | Round(f(n)/(f(k)*f(n-k))) >;
%o [A141601(n,k): k in [0..n], n in [0..14]]; // _G. C. Greubel_, Sep 20 2024
%o (SageMath)
%o def f(n): return 1 if (n<2) else factorial(n)*binomial(n,2)
%o def A141601(n,k): return round(f(n)/(f(k)*f(n-k)))
%o flatten([[A141601(n,k) for k in range(n+1)] for n in range(15)]) # _G. C. Greubel_, Sep 20 2024
%Y Cf. A141600.
%K nonn,easy,tabl
%O 0,5
%A _Roger L. Bagula_ and _Gary W. Adamson_, Aug 21 2008
%E Edited, and new name, by _G. C. Greubel_, Sep 20 2024