A107867 - OEIS

%I #6 Jan 17 2020 23:02:33

%S 1,2,1,6,3,1,35,15,4,1,330,120,28,5,1,4368,1365,286,45,6,1,74613,

%T 20349,3876,560,66,7,1,1560780,376740,65780,8855,969,91,8,1,38608020,

%U 8347680,1344904,169911,17550,1540,120,9,1,1101716330,215553195,32224114

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

%C Remarkably, the following matrix products are all equal to A107876: A107862^-1*A107867 = A107867^-1*A107870 = A107870^-1*A107873.

%e Triangle begins:

%e 1;

%e 2,1;

%e 6,3,1;

%e 35,15,4,1;

%e 330,120,28,5,1;

%e 4368,1365,286,45,6,1;

%e 74613,20349,3876,560,66,7,1;

%e 1560780,376740,65780,8855,969,91,8,1; ...

%o (PARI) T(n,k)=binomial(n*(n-1)/2-k*(k-1)/2 +n-k+1,n-k)

%Y Cf. A099121, A107862, A107865, A107867, A107870, A107876.

%K nonn,tabl

%O 0,2

%A _Paul D. Hanna_, Jun 04 2005