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Search: id:A002316
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| A002316 |
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Related to Bernoulli numbers.
(Formerly M3941 N1624)
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+0
7
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| 1, 5, 26, 97, 265, 362, -1351, -13775, -70226, -262087, -716035, -978122, 3650401, 37220045, 189750626, 708158977, 1934726305, 2642885282, -9863382151, -100568547815, -512706121226, -1913445293767, -5227629760075, -7141075053842
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Denoted by beta_n by Lehmer.
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
B. C. Berndt, Ramanujan's Notebooks Part IV, Springer-Verlag, see p. 84.
D. H. Lehmer, Lacunary recurrence formulas for the numbers of Bernoulli and Euler, Annals Math., 36 (1935), 637-649.
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LINKS
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Index entries for two-way infinite sequences
Index entries for sequences related to Bernoulli numbers.
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FORMULA
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a(0)..a(11) are as given (with signs); for n >= 12, a(n)=-2702*a(n-6)-a(n-12).
G.f.: (2x^3+7x^2-x+1)/(x^4+6x^3+11x^2-6x+1).
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PROGRAM
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(PARI) {a(n)=if(n>=0, polcoeff( (1-x+7*x^2+2*x^3)/(1-6*x+11*x^2+6*x^3+x^4) +x*O(x^n), n), n=-1-n; (-1)^n*polcoeff( (2-7*x-x^2-x^3)/(1-6*x+11*x^2+6*x^3+x^4) +x*O(x^n), n) )} /* Michael Somos Mar 27 2005 */
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CROSSREFS
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a(n)=(-1)^n*A002317(-1-n).
Sequence in context: A166810 A079909 A047669 this_sequence A005499 A003583 A033115
Adjacent sequences: A002313 A002314 A002315 this_sequence A002317 A002318 A002319
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KEYWORD
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sign,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from James A. Sellers (sellersj(AT)math.psu.edu), Dec 23 1999
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