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A103932 Numerators of first difference of squares of harmonic numbers. 3
1, 5, 10, 47, 131, 71, 353, 1487, 6989, 1451, 82451, 42433, 1132133, 1158863, 236749, 4828073, 41781863, 42482563, 273253759, 277235737, 56204647, 18975625, 441730115, 670193263, 33874048171, 34224132367, 311048966203, 313970420453 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The corresponding denominators are given in A103933.

h(n+1) + h(n) = (n+1)*(h(n+1)^2 - h(n)^2), where h(n) is the n-th harmonic number. - Gary Detlefs, May 25 2012

LINKS

Table of n, a(n) for n=1..28.

W. Lang: Rationals.

FORMULA

a(n)=numerator(r(n)), with the rationals r(n)=H(n)^2-H(n-1)^2 where H(n)= A001008(n)/A002805(n), n>=1, H(0):=0.

G.f. for r(n): (log(1-x))^2 + dilog(1-x) where dilog(1-x)=polylog(2, x).

a(n)= Numerator(h(n)+h(n-1)), where h(n) is the n-th harmonic number. - Gary Detlefs, May 25 2012

MATHEMATICA

Array[ HarmonicNumber[#]^2&, 29, 0] // Differences // Numerator (* Jean-Fran├žois Alcover, Jul 09 2013 *)

CROSSREFS

Sequence in context: A103971 A270085 A035406 * A034190 A216390 A305476

Adjacent sequences:  A103929 A103930 A103931 * A103933 A103934 A103935

KEYWORD

nonn,easy,frac

AUTHOR

Wolfdieter Lang, Mar 24 2005

STATUS

approved

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Last modified May 6 03:40 EDT 2021. Contains 343580 sequences. (Running on oeis4.)