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%I #8 May 26 2024 16:12:30
%S 1,4,4,10,35,10,20,165,165,20,35,560,1330,560,35,56,1540,7140,7140,
%T 1540,56,84,3654,29260,57155,29260,3654,84,120,7770,98770,333375,
%U 333375,98770,7770,120,165,15180,287980,1543465,2667126,1543465,287980,15180,165
%N Triangle read by rows, T(n,k) = (binomial(n,k)^3 - binomial(n,k))/6 for k=1..n-1 and n >= 2.
%C This triangle was mentioned in A143420 with the wrong A-number A143419.
%e T(n,k) for n=2..7:
%e 1;
%e 4, 4;
%e 10, 35, 10;
%e 20, 165, 165, 20;
%e 35, 560, 1330, 560, 35;
%e 56, 1540, 7140, 7140, 1540, 56;
%p seq(print(n,seq((binomial(n,k)^3 - binomial(n,k))/6,k=1..n-1)),n=2..10);
%Y Cf. A143418, A143420.
%K nonn,easy,tabl
%O 2,2
%A _Georg Fischer_, May 23 2024