login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 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

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: A261347 A079909 A047669 * A293799 A211606 A005499

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified October 21 13:33 EDT 2017. Contains 293696 sequences.