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 A119937 Triangle of numbers related to the spectrum of the hydrogen (H) atom. 7
 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; text; internal format)
 OFFSET 2,1 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. LINKS W. Lang: First ten rows. FORMULA a(m,n) = r(m,n)*lcm_{k=1..m-1} seq(r(m,k)) with r(m,n) = 1/n^2 - 1/m^2 = A120072(m,n)/A120073(m,n), m >= 2, n = 1..m-1. EXAMPLE [3]; [32,5]; [135,27,7]; [3456,756,256,81]; [3500,800,300,125,44]; ... 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: A136582 A173649 A210648 * A254312 A304048 A324223 Adjacent sequences:  A119934 A119935 A119936 * A119938 A119939 A119940 KEYWORD nonn,easy,tabl AUTHOR Wolfdieter Lang, Jul 20 2006 STATUS approved

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Last modified October 15 04:33 EDT 2019. Contains 328026 sequences. (Running on oeis4.)