The Leibniz harmonic triangle is the number triangle given by
 |
(1)
|
(OEIS A003506), where each fraction is the sum of the two adjacent entries in the next row and the initial and final
entries in the 
th
row are given by 
, for positive integers 
.
The terms are given by the recurrences
 |  |  |
(2)
|
 |  |  |
(3)
|
where the second recurrence applies for 
. The terms are given explicitly by
 |  |  |
(4)
|
 |  |  |
(5)
|
where 
and 
is a binomial coefficient.
The denominators in the second diagonals are the pronic numbers 6, 12, 20, 30, 42, 56, 72, 90, 110, 132, ... (OEIS A002378). A sorted list of all possible denominators of non-boundary entries in the triangle is given by 6, 12, 20, 30, 42, 56, 60, 72, 90, 105, 110, ... (OEIS A007622).
The row sums are given by 1, 1, 5/6, 2/3, 8/15, 13/30, 151/420, ... (OEIS A046878 and A046879).
The sums of the denominators
in the 
th
row are given by 
, giving the first few as 1, 4, 12, 32, 80, 192,
448, ... (OEIS A001787).
