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A119937
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Triangle of numbers related to the spectrum of the hydrogen (H) atom.
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7
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3, 32, 5, 135, 27, 7, 3456, 756, 256, 81, 3500, 800, 300, 125, 44, 172800, 40500, 16000, 7425, 3456, 1300, 694575, 165375, 67375, 33075, 17199, 8575, 3375, 6272000, 1509200, 627200, 318500, 175616, 98000, 51200
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 2,1
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COMMENTS
| The rational number triangle r(m,n):=A120072(m,n)/A120073(m,n), used to compute the spectral series of the hydrogen atom, is mapped to this nonnegative number triangle by multiplying the least common multiples (LCM) for each row m.
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LINKS
| W. Lang: First ten rows.
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FORMULA
| a(m,n) = r(m,n)*LCM(seq(r(m,k),k = 1..m-1)) with r(m,n) = 1/n^2 - 1/m^2 = A120072(m,n)/A120073(m,n), m>= 2, n = 1..m-1.
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EXAMPLE
| [3]; [32,5]; [135,27,7]; [3456,756,256,81]; [3500,800,300,125,44]; ...
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CROSSREFS
| The LCM sequence which has been used here is [4, 36, 144, 3600, 3600, 176400, 705600, 6350400, 6350400, 768398400, ...]= A051418(m)= (A003418(m))^2 = (2*A025555(m-1))^2, m>=2.
The row sums give A119938.
Sequence in context: A005042 A136582 A173649 * A197368 A114257 A197524
Adjacent sequences: A119934 A119935 A119936 * A119938 A119939 A119940
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KEYWORD
| nonn,easy,tabl
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AUTHOR
| Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Jul 20 2006
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