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A002316 Related to Bernoulli numbers.
(Formerly M3941 N1624)
6
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.

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).

LINKS

Table of n, a(n) for n=0..23.

Index entries for two-way infinite sequences

Index entries for sequences related to Bernoulli numbers.

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

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: A261347 A079909 A047669 * A211606 A005499 A185552

Adjacent sequences:  A002313 A002314 A002315 * A002317 A002318 A002319

KEYWORD

sign,easy

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from James A. Sellers, Dec 23 1999

STATUS

approved

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Last modified August 17 07:59 EDT 2017. Contains 290635 sequences.