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Search: id:A101627
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| A101627 |
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Numerator of partial sums of a certain series. |
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+0
5
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| 1, 39, 241, 34883, 14039, 1516871, 7601151, 875425657, 7887002813, 7095769757767, 14199583385459, 75087685321529, 75113436870869, 927229349730873529, 927436191807263569, 305182576081725442901
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OFFSET
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1,2
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COMMENT
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The denominators are given in A101628.
Second member (m=3) of a family defined in A101028.
The limit s=lim(s(n),n->infty) with the s(n) defined below equals 8*sum(Zeta(2*k+1)/3^(2*k),k=1..infty) with Euler's (or Riemann's) Zeta function. This limit is 12*(ln(3)-1) = 1.18334746...; see the Abramowitz-Stegun (given in A101028) reference p. 259, eq. 6.3.15 with z=1/3 together with p. 258.
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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, December 1972 [alternative scanned copy].
W. Lang: Rationals s(n) and more.
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FORMULA
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a(n)=numerator(s(n)) with s(n)=24*sum(1/((3*k-1)*(3*k)*(3*k+1)), k=1..n).
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EXAMPLE
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s(3)= 24*(1/(2*3*4)+ 1/(5*6*7) + 1/(8*9*10)) = 241/210, hence a(3)=241 and A101628(3)=210.
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CROSSREFS
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Cf. A101028, A101629, A101631 members m=2, 4, 5, resp.
Sequence in context: A105838 A124619 A068975 this_sequence A070146 A061169 A077454
Adjacent sequences: A101624 A101625 A101626 this_sequence A101628 A101629 A101630
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KEYWORD
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nonn,frac,easy
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Dec 23 2004
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