a(n,m) tabl head (triangle) for A119937 (rational triangle A120072/A120073, used for hydrogen spectrum, made integer) n\m 1 2 3 4 5 6 7 8 9 10 ... 2 3 0 0 0 0 0 0 0 0 0 3 32 5 0 0 0 0 0 0 0 0 4 135 27 7 0 0 0 0 0 0 0 5 3456 756 256 81 0 0 0 0 0 0 6 3500 800 300 125 44 0 0 0 0 0 7 172800 40500 16000 7425 3456 1300 0 0 0 0 8 694575 165375 67375 33075 17199 8575 3375 0 0 0 9 6272000 1509200 627200 318500 175616 98000 51200 20825 0 0 10 6286896 1524096 642096 333396 190512 112896 66096 35721 14896 0 11 762048000 185749200 79027200 41674500 24385536 14994000 9331200 5655825 3136000 1333584 . . . ############################################################################################################## The row sums give: [3,37,169,4549,4769,241481,989549,9072541,9206605,1127335045,...] = A119938(m),m>=2. The main diagonal gives:[3,5,7,81,44,1300,3375,20825,14896,1333584,,...] = A119939(m,m-1), m>=2. The column n=1 gives: [3,32,135,3456,3500,172800,694575,6272000,6286896,762048000,...] = A119940(m), m>=2. The column n=2 gives: [5,27,756,800,40500,165375,1509200,1524096,185749200,186763500,...] = A119941(m), m>=3. The column n=3 gives: [7,256,300,16000,67375,627200,642096,79027200,80041500,...] = A119942(m), m>=4. The column n=3 gives: [81,125,7425,33075,318500,333396,41674500,42688800,7347809700,,,,] = A119943(m), m>=5. ... ############################################################################################################### The LCM (least common multiple) sequence which has been used in producing this integer triange is [4, 36, 144, 3600, 3600, 176400, 705600, 6350400, 6350400, 768398400,...]= squares of (2*A025555(m-1))^2,m>=2 (conjecture). ############################################## e.o.f. ###########################################################