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A133002
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Numerators of Blandin-Diaz compositional Bernoulli numbers (B^S)_1,n.
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2
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1, -1, 5, -1, 139, -1, 859, 71, -9769, 233, -6395527, 145069, -304991568097, -95164619917, 119780081383, -3046785293, 4002469707564917, -102407337854027, 1286572077762833639, 219276930957009857, -20109624681057406222913, 1651690537394493957719
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OFFSET
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0,3
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COMMENTS
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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
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LINKS
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FORMULA
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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
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EXAMPLE
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1, -1/4, 5/72, -1/48, 139/21600, -1/540, 859/2540160, 71/483840, -9769/36288000 (corrected by Daniel Suteu, Feb 24 2018).
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MATHEMATICA
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CROSSREFS
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KEYWORD
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sign,frac
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AUTHOR
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EXTENSIONS
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Corrected the sign of a(0) and a(3) by Daniel Suteu, Feb 24 2018
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STATUS
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approved
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