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A133002 Numerators of Blandin-Diaz compositional Bernoulli numbers (B^S)_1,n. 2
1, -1, 5, -1, 139, -1, 859, 71, -9769, 233, -6395527, 145069, -304991568097, -95164619917, 119780081383, -3046785293, 4002469707564917, -102407337854027, 1286572077762833639, 219276930957009857, -20109624681057406222913, 1651690537394493957719 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Denominators are A133003. "Bernoulli numbers for S are shown in the table."

The signs of a(0) and a(3) are wrong in table of p. 11 of Bandin article. -  Daniel Suteu, Feb 24 2018

LINKS

Daniel Suteu, Table of n, a(n) for n = 0..200

Hector Blandin and Rafael Diaz, Compositional Bernoulli numbers, arXiv:0708.0809 [math.CO], 2007-2008, p. 11, 1st table.

FORMULA

a(n) = numerator(f(n) * n!), where f(0) = 1, f(n) = -Sum_{k=0..n-1} f(k) / ((n-k+1)!)^2. - Daniel Suteu, Feb 23 2018

EXAMPLE

1, -1/4, 5/72, -1/48, 139/21600, -1/540, 859/2540160, 71/483840, -9769/36288000 (corrected by Daniel Suteu, Feb 24 2018).

MATHEMATICA

f[0] = 1; f[n_] := f[n] = -Sum[f[k]/((n-k+1)!)^2, {k, 0, n-1}]; Table[f[n]*n! // Numerator, {n, 0, 21}] (* Jean-Fran├žois Alcover, Feb 25 2018, after Daniel Suteu *)

CROSSREFS

Cf. A132092, A132093, A132094, A132095, A132096, A132097, A132098, A132099.

Cf. A133000, A133001, A133003, A133004, A133005.

Sequence in context: A294260 A113114 A099740 * A272755 A293572 A294257

Adjacent sequences:  A132999 A133000 A133001 * A133003 A133004 A133005

KEYWORD

sign,frac

AUTHOR

Jonathan Vos Post, Aug 09 2007

EXTENSIONS

Corrected the sign of a(0) and a(3) by Daniel Suteu, Feb 24 2018

Terms beyond a(8) from Daniel Suteu, Feb 24 2018

STATUS

approved

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Last modified August 10 19:52 EDT 2020. Contains 336381 sequences. (Running on oeis4.)