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 A002316 Related to Bernoulli numbers. (Formerly M3941 N1624) 7
 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; text; internal format)
 OFFSET 0,2 COMMENTS Denoted by beta_n by Lehmer. REFERENCES B. C. Berndt, Ramanujan's Notebooks Part IV, Springer-Verlag, see p. 84. 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). LINKS Robert Israel, Table of n, a(n) for n = 0..1746 D. H. Lehmer, Lacunary recurrence formulas for the numbers of Bernoulli and Euler, Annals Math., 36 (1935), 637-649. Index entries for linear recurrences with constant coefficients, signature (6,-11,-6,-1). 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). - Harvey P. Dale, Jun 13 2011 MAPLE f:= gfun:-rectoproc({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)}, a(n), remember): map(f, [\$0..25]); # Robert Israel, Aug 23 2017 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] (* Harvey P. Dale, Jun 13 2011 *) 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 */ CROSSREFS a(n) = (-1)^n*A002317(-1-n). Sequence in context: A301518 A047669 A297689 * A293799 A211606 A005499 Adjacent sequences:  A002313 A002314 A002315 * A002317 A002318 A002319 KEYWORD sign,easy AUTHOR EXTENSIONS More terms from James A. Sellers, Dec 23 1999 STATUS approved

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Last modified June 21 06:24 EDT 2021. Contains 345358 sequences. (Running on oeis4.)