A174413 - OEIS

%I #24 Sep 04 2019 21:07:15

%S 4,36,9,144,16,16,400,225,100,25,900,144,12,9,36,1764,1225,784,441,

%T 196,49,3136,576,1600,64,576,64,64,5184,3969,324,2025,1296,81,324,81,

%U 8100,1600,4900,225,100,400,900,25,100,12100,9801,7744,5929,4356,3025,1936,1089,484,121

%N Triangle T(n,m) with the denominator of 1/(n-m)^2-1/n^2, read by rows, 1<=m<n.

%C Obtained by deleting the last entry in each row of A061036 or by reversing rows in A120073.

%H Alois P. Heinz, <a href="/A174413/b174413.txt">Table of n, a(n) for n = 2..2017</a>

%e Triangle T(n,m) begins:

%e      4,

%e     36,    9,

%e    144,   16,   16,

%e    400,  225,  100,  25,

%e    900,  144,   12,   9,  36,

%e   1764, 1225,  784, 441, 196, 49,

%e   3136,  576, 1600,  64, 576, 64, 64,

%p A174413 := proc(n,m) 1/(n-m)^2-1/n^2 ; denom(%) ; end proc:

%p seq(seq(A174413(n, k), k=1..n-1), n=2..11); # _R. J. Mathar_, Jan 27 2011

%t T[n_, m_] := Denominator[1/(n - m)^2 - 1/n^2];

%t Table[T[n, m], {n, 2, 11}, {m, 1, n-1}] // Flatten (* _Jean-François Alcover_, May 18 2018 *)

%Y Cf. A165441, A172370 (numerators).

%K nonn,frac,tabl,look,easy

%O 2,1

%A _Paul Curtz_, Mar 19 2010