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Search: id:A096617
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| A096617 |
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Numerator of n*HarmonicNumber[n]. |
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+0
4
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| 1, 3, 11, 25, 137, 147, 363, 761, 7129, 7381, 83711, 86021, 1145993, 1171733, 1195757, 2436559, 42142223, 42822903, 275295799, 279175675, 56574159, 19093197, 444316699, 1347822955, 34052522467, 34395742267, 312536252003
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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a(1) = 1, a(n) = Numerator[ H(n) / H(n-1) ], where H(n) = HarmonicNumber[n] = A001008(n)/A002805(n). (Alexander Adamchuk (alex(AT)kolmogorov.com), Oct 29 2004)
Sampling a population of n distinct elements with replacement, n HarmonicNumber[n] is the expectation of the sample size for the acquisition of all n distinct elements. (Franz Vrabec (franz.vrabec(AT)aon.at), Oct 30 2004)
p^2 divides a(p-1) for prime p>3. - Alexander Adamchuk (alex(AT)kolmogorov.com), Jul 16 2006
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REFERENCES
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W. Feller, An Introduction to Probability Theory and Its Applications, Vol. I, 2nd Ed. 1957, p. 211, formula (3.3)
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LINKS
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Eric Weisstein's World of Mathematics, Complete Set
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FORMULA
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abs(Stirling1(n+1, 2))/(n-1)!. - Vladeta Jovovic (vladeta(AT)eunet.rs), Jul 06 2004
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EXAMPLE
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1, 3, 11/2, 25/3, 137/12, 147/10, 363/20, 761/35, 7129/280, ...
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MAPLE
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ZL:=n->sum(sum(1/i, i=1..n), j=1..n): a:=n->floor(numer(ZL(n))): seq(a(n), n=1..27); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 14 2007
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MATHEMATICA
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Numerator[Table[(Sum[(1/k), {k, 1, n}]/Sum[(1/k), {k, 1, n-1}]), {n, 1, 20}]] (Alexander Adamchuk (alex(AT)kolmogorov.com), Oct 29 2004)
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CROSSREFS
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Cf. A027611.
Cf. A001008, A002805.
Sequence in context: A060746 A111935 A001008 this_sequence A025529 A124078 A096795
Adjacent sequences: A096614 A096615 A096616 this_sequence A096618 A096619 A096620
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KEYWORD
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nonn,frac
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AUTHOR
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Eric Weisstein (eric(AT)weisstein.com), Jul 01, 2004
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