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A140351
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Numerator of the coefficient [x^1] of the Bernoulli twin number polynomial C(n,x).
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4
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1, 0, -1, -1, -1, 1, 1, -1, -3, 3, 5, -5, -691, 691, 35, -35, -3617, 3617, 43867, -43867, -1222277, 1222277, 854513, -854513, -1181820455, 1181820455, 76977927, -76977927, -23749461029, 23749461029, 8615841276005, -8615841276005, -84802531453387, 84802531453387
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,9
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COMMENTS
| The Bernoulli twin number polynomials C(n,x) are defined in A129378.
I call the full fraction [x^1]C(n,x) the secondary Bernoulli twin numbers.
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EXAMPLE
| The coefficients [x^m]C(n,x) are a table of fractions:
1 ;
-1/2, 1;
-1/3, 0, 1;
-1/6, -1/2, 1/2, 1;
-1/30,-1/2, -1/2, 1, 1;
1/30, -1/6, -1,-1/3, 3/2, 1;
1/42, 1/6, -1/2, -5/3, 0, 2, 1;
-1/42, 1/6, 1/2, -7/6, -5/2, 1/2, 5/2, 1;
-1/30, -1/6, 2/3, 7/6, -7/3, -7/2, 7/6, 3, 1;
1/30, -3/10, -2/3, 2, 7/3, -21/5, -14/3, 2, 7/2, 1;
5/66, 3/10, -3/2, -2, 5, 21/5, -7, -6, 3, 4, 1; ...
This sequence here contains the numerators of the second column.
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MAPLE
| C := proc(n, x) if n = 0 then 1; else add(binomial(n-1, j-1)* bernoulli(j, x), j=1..n) ; expand(%) ; end if ; end proc:
A140351 := proc(n) coeff(C(n, x), x, 1) ; numer(%) ; end proc: seq(A140351(n), n=1..80) ; # R. J. Mathar, Nov 22 2009
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CROSSREFS
| Cf. A129826
Sequence in context: A014414 A087745 A087756 * A128444 A204250 A131948
Adjacent sequences: A140348 A140349 A140350 * A140352 A140353 A140354
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KEYWORD
| frac,sign
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AUTHOR
| Paul Curtz (bpcrtz(AT)free.fr), May 30 2008, Jun 23 2008
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EXTENSIONS
| Edited and extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 22 2009
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