|
Search: id:A096617
|
|
|
| A096617 |
|
Numerator of n*HarmonicNumber[n]. |
|
+0
4
|
|
| 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)
|
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
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)planetuniqa.at), Oct 30 2004)
p^2 divides a(p-1) for prime p>3. - Alexander Adamchuk (alex(AT)kolmogorov.com), Jul 16 2006
|
|
REFERENCES
|
W. Feller, An Introduction to Probability Theory and Its Applications, Vol. I, 2nd Ed. 1957, p. 211, formula (3.3)
|
|
LINKS
|
Eric Weisstein's World of Mathematics, Complete Set
|
|
FORMULA
|
abs(Stirling1(n+1, 2))/(n-1)!. - Vladeta Jovovic (vladeta(AT)eunet.rs), Jul 06 2004
|
|
EXAMPLE
|
1, 3, 11/2, 25/3, 137/12, 147/10, 363/20, 761/35, 7129/280, ...
|
|
MAPLE
|
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
|
|
MATHEMATICA
|
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)
|
|
CROSSREFS
|
Cf. A027611.
Cf. A001008, A002805.
Adjacent sequences: A096614 A096615 A096616 this_sequence A096618 A096619 A096620
Sequence in context: A060746 A111935 A001008 this_sequence A025529 A124078 A096795
|
|
KEYWORD
|
nonn,frac
|
|
AUTHOR
|
Eric Weisstein (eric(AT)weisstein.com), Jul 01, 2004
|
|
|
Search completed in 0.002 seconds
|
