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A002316
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Related to Bernoulli numbers.
(Formerly M3941 N1624)
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6
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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; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Denoted by beta_n by Lehmer.
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REFERENCES
| 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.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| Index entries for two-way infinite sequences
Index entries for sequences related to Bernoulli numbers.
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FORMULA
| 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).
a(0)=1, a(1)=5, a(2)=26, a(3)=97, a(n)=6*a(n-1)-11*a(n-2)-6*a(n-3)-a(n-4) [From Harvey P. Dale, June 13 2011]
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MATHEMATICA
| LinearRecurrence[{6, -11, -6, -1}, {1, 5, 26, 97}, 30] (* or *) CoefficientList[ Series[(2x^3+7x^2-x+1)/(x^4+6x^3+11x^2-6x+1), {x, 0, 30}], x] (* From Harvey P. Dale, June 13 2011 *)
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PROG
| (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
| a(n)=(-1)^n*A002317(-1-n).
Sequence in context: A166810 A079909 A047669 * A005499 A185552 A171702
Adjacent sequences: A002313 A002314 A002315 * A002317 A002318 A002319
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KEYWORD
| sign,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from James A. Sellers (sellersj(AT)math.psu.edu), Dec 23 1999
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