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A132095
Denominators of expansion of e.g.f. x^2/(2*(cos(x)-1)), even powers only.
4
1, 6, 10, 42, 30, 22, 2730, 6, 34, 798, 330, 46, 2730, 6, 290, 14322, 510, 2, 54834, 6, 4510, 1806, 690, 94, 46410, 66, 530, 798, 174, 118, 56786730, 6, 170, 64722, 30, 1562, 140100870, 6, 2, 474, 230010, 166, 3404310, 6, 20470, 272118, 1410, 2, 900354, 6
OFFSET
1,2
COMMENTS
Numerators and denominators given only for even n (odd n have numerators = 0).
REFERENCES
Hector Blandin and Rafael Diaz, Compositional Bernoulli numbers , Afr. Diaspora J. Math., Volume 7, Number 2 (2008).
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* A132094(n)/(a(n)*x^(2*n-1)) as x -> infinity. - 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
A132095 := proc(n) add( 2*(-1)^i*x^(2*i)/(2*i+2)!, i=0..n/2+1) ; denom(coeftayl(-1/%, x=0, n)*n!) ; end: for n from 0 to 46 by 2 do printf("%d, ", A132095(n)) ; od: # R. J. Mathar, Oct 18 2007
MATHEMATICA
A132095[n_] := (s = Sum[ 2*(-1)^i*x^(2*i)/(2*i + 2)!, {i, 0, n/2 + 1}] ; Denominator[SeriesCoefficient[-1/s, {x, 0, n}]*n!]) ;
Table[ A132095[n], {n, 0, 100, 2}] (* Jean-François Alcover, Nov 24 2017, after R. J. Mathar *)
PROG
(PARI) my(x='x+O('x^100), v=apply(denominator, Vec(serlaplace(x^2/(2*(cos(x)-1)))))); vector(#v\2, k, v[2*k-1]) \\ Michel Marcus, Jan 25 2024
CROSSREFS
Numerators are A132094.
Sequence in context: A094890 A213477 A047178 * A332441 A153328 A068588
KEYWORD
frac,nonn
AUTHOR
Jonathan Vos Post, Aug 09 2007
EXTENSIONS
More terms from R. J. Mathar, Oct 18 2007 and Oct 20 2009
Meaningful name from Joerg Arndt, Jan 25 2024
STATUS
approved