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A035048
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Numerators of alternating sum transform (PSumSIGN) of Harmonic numbers H(n) = A001008/A002805.
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3
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1, 1, 4, 3, 23, 11, 176, 25, 563, 137, 6508, 49, 88069, 363, 91072, 761, 1593269, 7129, 31037876, 7381, 31730711, 83711, 744355888, 86021, 3788707301, 1145993, 11552032628, 1171733, 340028535787, 1195757
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| p^2 divides a(2p-2) for prime p>3. a(2p-2)/p^2 = A061002(n) = A001008(p-1)/p^2 for prime p>2. - Alexander Adamchuk (alex(AT)kolmogorov.com), Jul 07 2006
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LINKS
| N. J. A. Sloane, Transforms
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FORMULA
| G.f. for A035048(n)/A035047(n) : log(1-x)/(x^2-1) - Benoit Cloitre (benoit7848c(AT)orange.fr), Jun 15 2003
a(n) = Numerator[Sum[(-1)^(k+1)*Sum[(-1)^(i+1)*1/i,{i,1,k}],{k,1,n}]]. - Alexander Adamchuk (alex(AT)kolmogorov.com), Jul 07 2006
G.f. for A035048(n)/A035047(n) : a(n)=(-1)^(n+1)*1/2*(log(2)+(-1)^(n+1)*(Euler+1/2*(psi(1+n/2)-psi(3/2+n/2))+psi(2+n))) - [Gerry Martens, Apr 28 2011]
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MATHEMATICA
| Numerator[Table[Sum[(-1)^(k+1)*Sum[(-1)^(i+1)*1/i, {i, 1, k}], {k, 1, n}], {n, 1, 50}]] - Alexander Adamchuk (alex(AT)kolmogorov.com), Jul 07 2006
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PROG
| (PARI) a(n)=numerator(polcoeff(log(1-x)/(x^2-1)+O(x^(n+1)), n))
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CROSSREFS
| Cf. A035047.
Cf. A002428.
Cf. A001008, A058313, A061002.
Sequence in context: A167479 A076589 A052039 * A189742 A072044 A127138
Adjacent sequences: A035045 A035046 A035047 * A035049 A035050 A035051
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KEYWORD
| nonn,easy,frac
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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