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 A002427 Numerator of (2n+1) B_{2n}, where B_n are the Bernoulli numbers. (Formerly M2510 N0993) 9
 1, 1, -1, 1, -3, 5, -691, 35, -3617, 43867, -1222277, 854513, -1181820455, 76977927, -23749461029, 8615841276005, -84802531453387, 90219075042845, -26315271553053477373, 38089920879940267, -261082718496449122051, 1520097643918070802691 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Doubled a(n+2)=-1,1,-3,5,-691,35, "gives" A140351(n+4) secondary Bernoulli twin numbers. Thanks to R. J. Mathar. [Paul Curtz, Nov 28 2009] REFERENCES A. Fletcher, J. C. P. Miller, L. Rosenhead and L. J. Comrie, An Index of Mathematical Tables. Vols. 1 and 2, 2nd ed., Blackwell, Oxford and Addison-Wesley, Reading, MA, 1962, Vol. 1, p. 73. 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 Seiichi Manyama, Table of n, a(n) for n = 0..314 (terms 0..100 from T. D. Noe) L. Euler, (E393) De summis serierum numeros Bernoullianos involventium, reprinted in: Opera Omnia. Teubner, Leipzig, 1911, Series (1), Vol. 15, p. 93. M. Kaneko, A recurrence formula for the Bernoulli numbers, Proc. Japan Acad., 71 A (1995), 192-193. EXAMPLE (n+1)*B_n gives the sequence 1, -1/2, 1/6, 0, -1/30, 0, 1/42, 0, -1/30, 0, 5/66, ... MAPLE gf := z / (1 - exp(-z)): ser := series(gf, z, 84): seq(numer((n+1)!*coeff(ser, z, n)), n=0..42, 2); # Peter Luschny, Aug 29 2020 MATHEMATICA Table[Numerator[2(2n+1)BernoulliB[2n]], {n, 1, 30}] PROG (PARI) a(n) = numerator((2*n+1)*bernfrac(2*n)); \\ Michel Marcus, Aug 06 2017 (Magma) [Numerator((2*n+1)*Bernoulli(2*n)): n in [1..30]]; // G. C. Greubel, Jul 03 2019 (Sage) [numerator((2*n+1)*bernoulli(2*n)) for n in (1..30)] # G. C. Greubel, Jul 03 2019 CROSSREFS Denominators are in A006955. Cf. A050925/A050932, A000367/A002445. Sequence in context: A354245 A247699 A320939 * A350036 A136134 A119497 Adjacent sequences:  A002424 A002425 A002426 * A002428 A002429 A002430 KEYWORD sign,easy,nice,frac AUTHOR STATUS approved

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Last modified November 26 03:08 EST 2022. Contains 358353 sequences. (Running on oeis4.)