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A132094 Numerators of Blandin-Diaz compositional Bernoulli numbers (B^cos)_2,n. 6
-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

Denominators are A132095. 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

(((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* a(n)/(A132095(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

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

CROSSREFS

Cf. A132092-A132106.

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

STATUS

approved

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Last modified September 21 19:57 EDT 2020. Contains 337273 sequences. (Running on oeis4.)