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Search: id:A043303
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| A043303 |
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Numerator of B(4n+2)/(2n+1) where B(m) are the Bernoulli numbers. |
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+0
2
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| 1, 1, 1, 1, 43867, 77683, 657931, 1723168255201, 151628697551, 154210205991661, 1520097643918070802691, 25932657025822267968607, 19802288209643185928499101, 29149963634884862421418123812691
(list; graph; listen)
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OFFSET
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0,5
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COMMENT
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Note that numerator of B(2n)/n is odd so B(2n)/(2n), B(2n)/(4n), etc. have the same numerators. - Michael Somos, Feb 01, 2004
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REFERENCES
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Bruce Berndt, Ramanujan's Notebooks Part II, Springer-Verlag; see Infinite series, p. 262.
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FORMULA
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B(4n+2)/(8n+4)=sum(k=1, infinity, k^(4n+1)/(exp(2Pi*k)-1))
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PROGRAM
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(PARI) a(n)=if(n<0, 0, numerator(bernfrac(4*n+2)/(2*n+1)))
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CROSSREFS
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Cf. A043304. a(n)=A001067(2n+1).
Sequence in context: A140931 A045157 A037147 this_sequence A049205 A015388 A115959
Adjacent sequences: A043300 A043301 A043302 this_sequence A043304 A043305 A043306
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KEYWORD
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easy,frac,nonn
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 04 2002
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