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A006955
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Denominator of (2n+1) B_{2n}, where B_n are the Bernoulli numbers.
(Formerly M1562)
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4
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1, 2, 6, 6, 10, 6, 210, 2, 30, 42, 110, 6, 546, 2, 30, 462, 170, 6, 51870, 2, 330, 42, 46, 6, 6630, 22, 30, 798, 290, 6, 930930, 2, 102, 966, 10, 66, 1919190, 2, 30, 42, 76670, 6, 680862, 2, 690, 38874, 470, 6, 46410, 2, 330, 42, 106, 6, 1919190
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Also denominators of asymptotic expansion of polygamma function psi''(z).
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REFERENCES
| M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, Tenth Printing, 1972, p. 260, (6.4.13).
L. Euler, (E393) De summis serierum numeros Bernoullianos involventium, reprinted in: Opera Omnia. Teubner, Leipzig, 1911, Series (1), Vol. 15, p. 93.
A. Fletcher, J. C. P. Miller, L. Rosenhead and L. J. Comrie, An Index of Mathematical Tables. Vols. 1 and 2, 2nd ed., Blackwell, Oxford and Addison-Wesley, Reading, MA, 1962, Vol. 1, p. 73.
M. Kaneko, "A recurrence formula for the Bernoulli numbers", Proc. Japan Acad., 71 A (1995), 192-193.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| T. D. Noe, Table of n, a(n) for n=0..1000
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, Tenth Printing, 1972, p. 260, (6.4.13).
Index entries for sequences related to Bernoulli numbers.
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EXAMPLE
| (n+1)*B_n gives the sequence 1, -1/2, 1/6, 0, -1/30, 0, 1/42, 0, -1/30, 0, 5/66, ...
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MATHEMATICA
| Denominator[Table[(2n+1)BernoulliB[2n], {n, 0, 60}]] (* From Harvey P. Dale, Nov 03 2011 *)
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CROSSREFS
| Numerators are in A002427. Cf. A050925/A050932, A000367/A002445, A006956.
Sequence in context: A005869 A021978 A141377 * A196053 A063210 A114718
Adjacent sequences: A006952 A006953 A006954 * A006956 A006957 A006958
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KEYWORD
| nonn,frac,easy,nice
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AUTHOR
| Simon Plouffe, N. J. A. Sloane (njas(AT)research.att.com).
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