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A132095 Denominators of Blandin-Diaz compositional Bernoulli numbers (B^cos)_2,n. 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Numerators are A132094. 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, Aug 06 2007, p. 8, 2nd table. [Dead link]

Hector Blandin and Rafael Diaz, Compositional Bernoulli numbers, arXiv:0708.0809 [math.CO], 2007-2008, p. 8, 2nd table.

FORMULA

(((x^2)/2!)/(cos(x)-1) = SUM[n=0..infinity] (B^cos)_2,n ((x^n)/n!).

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-Fran├žois Alcover, Nov 24 2017, after R. J. Mathar *)

CROSSREFS

Cf. A132092-A132106.

Sequence in context: A094890 A213477 A047178 * A332441 A153328 A068588

Adjacent sequences:  A132092 A132093 A132094 * A132096 A132097 A132098

KEYWORD

frac,nonn

AUTHOR

Jonathan Vos Post, Aug 09 2007

EXTENSIONS

More terms from R. J. Mathar, Oct 18 2007 and Oct 20 2009

STATUS

approved

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Last modified August 7 12:13 EDT 2020. Contains 336276 sequences. (Running on oeis4.)