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The arithmetic mean of the first and the second Bernoulli numbers are the associate Bernoulli numbers: B0 = 1, B1 = 0, B2 = 1/6, B3 = 0, B4 = -1/30, A176327 / A027642 in OEIS. Via the second row of its inverse Akiyama-Tanigawa transform (sequence A177427 in OEIS), they lead to Balmer series A061037 / A061038.
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