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
Robert Israel, Table of n, a(n) for n = 1..1000
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!]) ;
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
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