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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
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
Wolfdieter 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
MAPLE
H:= Vector(51):
for i from 2 to 51 do H[i]:= H[i-1]+1/(i-1) od:
HS:= map(t -> t^2, H):
convert(map(numer, HS[2..-1]-HS[1..-2]), list); # Robert Israel, Sep 27 2023
MATHEMATICA
Array[ HarmonicNumber[#]^2&, 29, 0] // Differences // Numerator (* Jean-François Alcover, Jul 09 2013 *)
CROSSREFS
Sequence in context: A103971 A270085 A035406 * A034190 A216390 A305476
KEYWORD
nonn,easy,frac
AUTHOR
Wolfdieter Lang, Mar 24 2005
STATUS
approved