A002317 Related to Genocchi numbers. (Formerly M1341 N0514)

2, 5, 7, -26, -265, -1351, -5042, -13775, -18817, 70226, 716035, 3650401, 13623482, 37220045, 50843527, -189750626, -1934726305, -9863382151, -36810643322, -100568547815, -137379191137, 512706121226, 5227629760075, 26650854921601

Offset

0,1

Comments

Denoted by beta'_n by Lehmer.

References

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

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

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 linear recurrences with constant coefficients, signature (6,-11,-6,-1).

Formula

G.f.: (2-7*x-x^2-x^3)/(1-6*x+11*x^2+6*x^3+x^4).

a(n) = -2702*a(n-6) - a(n-12).

Mathematica

a[0] = 2; a[1] = 5; a[2] = 7; a[3] = -26; a[n_] := a[n] = -a[n-4] - 6*a[n-3] - 11*a[n-2] + 6*a[n-1]; Table[a[n], {n, 0, 23}] (* Jean-François Alcover, May 23 2013 *)
CoefficientList[Series[(2 - 7 x - x^2 - x^3) / (1 - 6 x + 11 x^2 + 6 x^3 + x^4), {x, 0, 40], x] (* Vincenzo Librandi, Jul 21 2013 *)
LinearRecurrence[{6, -11, -6, -1}, {2, 5, 7, -26}, 40] (* Harvey P. Dale, Jun 04 2017 *)

Prog

(PARI) {a(n)=if(n>=0, polcoeff( (2-7*x-x^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( (1-x+7*x^2+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*A002316(-1-n).

Sequence in context: A041245 A042159 A071898 * A343596 A137098 A082013

Adjacent sequences: A002314 A002315 A002316 * A002318 A002319 A002320

Keyword

sign,easy

Author

N. J. A. Sloane

Status

approved