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A096617 Numerator of n*HarmonicNumber(n). 5
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; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(1) = 1, a(n) = Numerator( H(n) / H(n-1) ), where H(n) = HarmonicNumber(n) = A001008(n)/A002805(n). - Alexander Adamchuk, 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, Oct 30 2004

p^2 divides a(p-1) for prime p>3. - Alexander Adamchuk, 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

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Eric Weisstein's World of Mathematics, Complete Set

FORMULA

abs(Stirling1(n+1, 2))/(n-1)!. - Vladeta Jovovic, Jul 06 2004

a(n) also equals numerator of integral(1-(1-exp(-t/n])^n, {t, 0, infinity}). - Jean-François Alcover, Feb 17 2014

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, Jun 14 2007

MATHEMATICA

Numerator[Table[(Sum[(1/k), {k, 1, n}]/Sum[(1/k), {k, 1, n-1}]), {n, 1, 20}]] (Alexander Adamchuk, Oct 29 2004)

Table[n*HarmonicNumber[n] // Numerator, {n, 1, 27}]  (* Jean-François Alcover, Feb 17 2014 *)

PROG

(MAGMA) [Numerator(n*HarmonicNumber(n)): n in [1..40]]; // Vincenzo Librandi, Feb 19 2014

CROSSREFS

Cf. A027611, A001008, A002805.

Differs from A025529 at 7th term.

Sequence in context: A175441 A001008 A231606 * A025529 A124078 A096795

Adjacent sequences:  A096614 A096615 A096616 * A096618 A096619 A096620

KEYWORD

nonn,frac

AUTHOR

Eric W. Weisstein, Jul 01 2004

STATUS

approved

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Last modified February 24 14:41 EST 2018. Contains 299623 sequences. (Running on oeis4.)