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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
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.
Sequence in context: A242503 A116048 A120282 * A082878 A106506 A029649
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.)