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A164555
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Numerators of the "original" Bernoulli numbers.
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41
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1, 1, 1, 0, -1, 0, 1, 0, -1, 0, 5, 0, -691, 0, 7, 0, -3617, 0, 43867, 0, -174611, 0, 854513, 0, -236364091, 0, 8553103, 0, -23749461029, 0, 8615841276005, 0, -7709321041217, 0, 2577687858367, 0, -26315271553053477373, 0, 2929993913841559, 0, -261082718496449122051
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,11
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COMMENTS
| Apart from a sign flip in a(1), the same as A027641.
a(n) is also the numerator of the n-th term of the Binomial transform of the sequence of Bernoulli numbers, i.e., of the sequence of fractions A027641(n)/A027642(n).
a(n)/A027642(n) with e.g.f. x/(1-exp(-x)) is the a-sequence for the Sheffer matrix A094645, see the W. Lang link under A006232 for Sheffer a- and z-sequences. [Wolfdieter Lang, Jun 20 2011]
a(n)/A027642(n) give also the row sums of the rational triangle of the coefficients of the Bernoulli polynomials A053382/A053383 (falling powers) or A196838/A196839 (rising powers). [Wolfdieter Lang, Oct 25 2011]
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LINKS
| Tom Rike, Sums of powers and Bernoulli numbers.
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CROSSREFS
| Sequence in context: A036946 A027641 * A176327 A129205 A098173 A180977
Adjacent sequences: A164552 A164553 A164554 * A164556 A164557 A164558
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KEYWORD
| sign,frac
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AUTHOR
| Paul Curtz (bpcrtz(AT)free.fr), Aug 15 2009
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EXTENSIONS
| Edited and extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 03 2009
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