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Search: id:A101631
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| A101631 |
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Numerator of partial sums of a certain series. |
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+0
5
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| 1, 37, 1069, 20575, 1346153, 1214756107, 20699705479, 850029466379, 19572345658457, 137116980686111, 411600123273343, 1482039573988769177, 456179332236626381, 32398234503565880731, 1199020509231104363863
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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 A101632.
Third member (m=5) of a family defined in A101028.
The limit s=lim(s(n),n->infinity) with the s(n) defined below equals 24*sum(Zeta(2*k+1)/5^(2*k),k=1..infinity) with Euler's (or Riemann's) Zeta function. This limit is -24*(gamma +Psi(1/5) +5/2 + Pi*cot(Pi/5)/2) = 1.1954056019...; see a comment in A101028 following from the Abramowitz-Stegun reference(given in A101028) p. 259, eq. 6.3.15 with z=1/5 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,5) and more.
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FORMULA
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a(n)=numerator(s(n)) with s(n)= 120*sum(1/((5*k-1)*(5*k)*(5*k+1)), k=1..n) = 24*sum(1/((5*k-1)*k*(5*k+1)), k=1..n).
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EXAMPLE
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s(3)= 120*(1/(4*5*6)+ 1/(9*10*11) + 1/(14*15*16)) = 1069/924, hence
a(3)=1069 and A101632(3)=924.
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CROSSREFS
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Cf. A101028, A101627, A101629, members 2, 3, 4, resp.
Adjacent sequences: A101628 A101629 A101630 this_sequence A101632 A101633 A101634
Sequence in context: A103724 A014935 A124155 this_sequence A005390 A099201 A006062
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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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