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 A132094 Numerators of expansion of e.g.f. x^2/(2*(cos(x)-1)), even powers only. 7
 -1, -1, -1, -5, -7, -15, -7601, -91, -3617, -745739, -3317609, -5981591, -5436374093, -213827575, -213745149261, -249859397004145, -238988952277727, -28354566442037, -26315271553053477373, -108409774812137683, -3394075340453838586663, -62324003400640902910331 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS Numerators and denominators given only for even n (odd n have numerators = 0). REFERENCES J. Riordan, Combinatorial Identities, Wiley, 1968, p. 199. See Table 3.3. LINKS Robert Israel, Table of n, a(n) for n = 1..288 Hector Blandin and Rafael Diaz, Compositional Bernoulli numbers, arXiv:0708.0809 [math.CO], 2007-2008, p. 8, 2nd table. FORMULA Asymptotic series 2*Psi(1,x) + x*Psi(2,x) ~ Sum_{n>=1} (-1)^n* a(n)/(A132095(n)*x^(2*n-1)) as x -> oo. - Robert Israel, May 27 2015 EXAMPLE -1, 0, -1/6, 0, -1/10, 0, -5/42, 0, -7/30, 0, -15/22, 0, -7601/2730, 0. MAPLE A132094 := proc(n) add( 2*(-1)^i*x^(2*i)/(2*i+2)!, i=0..n+1) ; numer(coeftayl(-1/%, x=0, n)*n!) ; end: for n from 0 to 46 by 2 do printf("%d, ", A132094(n)) ; od: # R. J. Mathar, Oct 18 2007 MATHEMATICA A132094[n_] := (s = Sum[ 2*(-1)^i*x^(2*i)/(2*i + 2)!, {i, 0, n + 1}]; Numerator[SeriesCoefficient[-1/s, {x, 0, n}]*n!]); Table[A132094[n], {n, 0, 46, 2}] (* Jean-François Alcover, Nov 24 2017, after R. J. Mathar *) PROG (PARI) my(x='x+O('x^50), v=apply(numerator, Vec(serlaplace(x^2/(2*(cos(x)-1)))))); vector(#v\2, k, v[2*k-1]) \\ Michel Marcus, Jan 25 2024 CROSSREFS Denominators are A132095. Cf. A132092-A132099. Sequence in context: A242503 A116048 A120282 * A082878 A106506 A029649 Adjacent sequences: A132091 A132092 A132093 * A132095 A132096 A132097 KEYWORD frac,sign AUTHOR Jonathan Vos Post, Aug 09 2007 EXTENSIONS More terms from R. J. Mathar, Oct 18 2007 Meaningful name from Joerg Arndt, Jan 25 2024 STATUS approved

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Last modified March 2 12:01 EST 2024. Contains 370467 sequences. (Running on oeis4.)