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%I #8 Aug 26 2019 15:12:35
%S 1,5,83,1945,49177,1833349,141933773,2422703191,23493728113,
%T 306193780933,920490263449,72844719575371,3136916685865153,
%U 97366698355411543,487364191723246127,26098860817171249607,496295891513328449033,1821113866092559163621
%N Denominator of the harmonic mean of the first n 9-gonal numbers.
%H Colin Barker, <a href="/A250549/b250549.txt">Table of n, a(n) for n = 1..800</a>
%e a(3) = 83 because the first 3 9-gonal numbers are [1,9,24], and 3/(1/1+1/9+1/24) = 216/83.
%t Module[{nn=20,p9},p9=PolygonalNumber[9,Range[nn]];Table[Denominator[ HarmonicMean[ Take[p9,n]]],{n,nn}]] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Aug 26 2019 *)
%o (PARI)
%o harmonicmean(v) = #v / sum(k=1, #v, 1/v[k])
%o s=vector(30); for(n=1, #s, s[n]=denominator(harmonicmean(vector(n, k, (7*k^2-5*k)/2)))); s
%Y Cf. A001106 (9-gonal numbers), A250548 (numerators).
%K nonn,frac
%O 1,2
%A _Colin Barker_, Nov 25 2014