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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
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
E.g.f. for fractions: x / (BesselI(0,2*sqrt(x)) - 1). - Ilya Gutkovskiy, Sep 01 2021
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-François Alcover, Feb 25 2018, after Daniel Suteu *)
CROSSREFS
Sequence in context: A099740 A362161 A359657 * A272755 A293572 A294257
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 March 29 11:45 EDT 2024. Contains 371278 sequences. (Running on oeis4.)