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A002317
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Related to Genocchi numbers.
(Formerly M1341 N0514)
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1
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2, 5, 7, -26, -265, -1351, -5042, -13775, -18817, 70226, 716035, 3650401, 13623482, 37220045, 50843527, -189750626, -1934726305, -9863382151, -36810643322, -100568547815, -137379191137, 512706121226, 5227629760075, 26650854921601
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OFFSET
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0,1
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COMMENTS
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Denoted by beta'_n by Lehmer.
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REFERENCES
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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).
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LINKS
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Table of n, a(n) for n=0..23.
Index entries for two-way infinite sequences
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FORMULA
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G.f.: (2-7x-x^2-x^3)/(1-6x+11x^2+6x^3+x^4). a(n)=-2702*a(n-6)-a(n-12).
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MATHEMATICA
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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 *)
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PROG
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(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 */
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CROSSREFS
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a(n)=(-1)^n*A002316(-1-n).
Sequence in context: A041245 A042159 A071898 * A137098 A082013 A171831
Adjacent sequences: A002314 A002315 A002316 * A002318 A002319 A002320
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KEYWORD
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sign,changed
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AUTHOR
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N. J. A. Sloane.
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STATUS
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approved
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