Search: id:A002316
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%I A002316 M3941 N1624
%S A002316 1,5,26,97,265,362,1351,13775,70226,262087,716035,978122,3650401,
%T A002316 37220045,189750626,708158977,1934726305,2642885282,9863382151,
%U A002316 100568547815,512706121226,1913445293767,5227629760075,7141075053842
%V A002316 1,5,26,97,265,362,-1351,-13775,-70226,-262087,-716035,-978122,3650401,
               37220045,
%W A002316 189750626,708158977,1934726305,2642885282,-9863382151,-100568547815,-512706121226,
%X A002316 -1913445293767,-5227629760075,-7141075053842
%N A002316 Related to Bernoulli numbers.
%C A002316 Denoted by beta_n by Lehmer.
%D A002316 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A002316 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A002316 B. C. Berndt, Ramanujan's Notebooks Part IV, Springer-Verlag, see p. 
               84.
%D A002316 D. H. Lehmer, Lacunary recurrence formulas for the numbers of Bernoulli 
               and Euler, Annals Math., 36 (1935), 637-649.
%H A002316 <a href="Sindx_Tu.html#2wis">Index entries for two-way infinite sequences</
               a>
%H A002316 <a href="Sindx_Be.html#Bernoulli">Index entries for sequences related 
               to Bernoulli numbers.</a>
%F A002316 a(0)..a(11) are as given (with signs); for n >= 12, a(n)=-2702*a(n-6)-a(n-12).
%F A002316 G.f.: (2x^3+7x^2-x+1)/(x^4+6x^3+11x^2-6x+1).
%o A002316 (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 */
%Y A002316 a(n)=(-1)^n*A002317(-1-n).
%Y A002316 Sequence in context: A166810 A079909 A047669 this_sequence A005499 A003583 
               A033115
%Y A002316 Adjacent sequences: A002313 A002314 A002315 this_sequence A002317 A002318 
               A002319
%K A002316 sign,easy
%O A002316 0,2
%A A002316 N. J. A. Sloane (njas(AT)research.att.com).
%E A002316 More terms from James A. Sellers (sellersj(AT)math.psu.edu), Dec 23 1999

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