cp's OEIS Frontend

A107867 Triangle, read by rows, where T(n,k) = C(n*(n-1)/2-k*(k-1)/2+n-k+1,n-k).

%I A107867 #6 Jan 17 2020 23:02:33
%S A107867 1,2,1,6,3,1,35,15,4,1,330,120,28,5,1,4368,1365,286,45,6,1,74613,
%T A107867 20349,3876,560,66,7,1,1560780,376740,65780,8855,969,91,8,1,38608020,
%U A107867 8347680,1344904,169911,17550,1540,120,9,1,1101716330,215553195,32224114
%N A107867 Triangle, read by rows, where T(n,k) = C(n*(n-1)/2-k*(k-1)/2+n-k+1,n-k).
%C A107867 Remarkably, the following matrix products are all equal to A107876: A107862^-1*A107867 = A107867^-1*A107870 = A107870^-1*A107873.
%e A107867 Triangle begins:
%e A107867 1;
%e A107867 2,1;
%e A107867 6,3,1;
%e A107867 35,15,4,1;
%e A107867 330,120,28,5,1;
%e A107867 4368,1365,286,45,6,1;
%e A107867 74613,20349,3876,560,66,7,1;
%e A107867 1560780,376740,65780,8855,969,91,8,1; ...
%o A107867 (PARI) T(n,k)=binomial(n*(n-1)/2-k*(k-1)/2 +n-k+1,n-k)
%Y A107867 Cf. A099121, A107862, A107865, A107867, A107870, A107876.
%K A107867 nonn,tabl
%O A107867 0,2
%A A107867 _Paul D. Hanna_, Jun 04 2005