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Search: id:A075180
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| A075180 |
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Denominators from e.g.f. 1/(1-exp(-x)) - 1/x. |
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+0
2
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| 2, 12, 1, 120, 1, 252, 1, 240, 1, 132, 1, 32760, 1, 12, 1, 8160, 1, 14364, 1, 6600, 1, 276, 1, 65520, 1, 12, 1, 3480, 1, 85932, 1, 16320, 1, 12, 1, 69090840, 1, 12, 1, 541200, 1, 75852, 1, 2760, 1, 564, 1, 2227680
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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Denominators of Riemann's -Zeta(-n), n>=0.
Numerators are +1, A060054(n+1), n>=1.
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REFERENCES
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M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, Tenth Printing, 1972, p. 807, combined eqs. 23.2.11,14 and 15.
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LINKS
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M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, Tenth Printing, 1972, p. 807, combined eqs. 23.2.11,14 and 15.
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FORMULA
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a(n)=denominator(-Zeta(-n))=denominator(((-1)^(n+1))*B(n+1)/(n+1)), n>=0, with Riemann's zeta function and the Bernoulli numbers B(n).
a(n)= denominators from e.g.f. (B(-x)-1)/x, with B(x)= x/(exp(x)-1), e.g.f. for Bernoulli numbers A027641(n)/A027642(n), n>=0.
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EXAMPLE
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1/2, 1/12, 0, -1/120, 0, 1/252, 0, -1/240, 0, 1/132, 0, -691/32760,...
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MAPLE
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a := n -> denom(bernoulli(n+1, 1)/(n+1)); [From Peter Luschny (peter(AT)luschny.de), Apr 22 2009]
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MATHEMATICA
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a[m_] := Sum[(-2)^(-k-1) k! StirlingS2[m, k], k, 0, m}]/(2^(m+1)-1); Table[Denominator[a[i]], {i, 0, 20}] [From Peter Luschny (peter(AT)luschny.de), Apr 29 2009]
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CROSSREFS
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A060054, A006232 with A006233.
Sequence in context: A082185 A113491 A107773 this_sequence A167164 A010239 A128268
Adjacent sequences: A075177 A075178 A075179 this_sequence A075181 A075182 A075183
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KEYWORD
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nonn,easy
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Sep 06, 2002
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