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Numerator of the harmonic mean of the first n 9-gonal numbers.
2

%I #10 Sep 30 2016 13:51:20

%S 1,9,216,6624,207000,9190800,825640200,16041009600,174445979400,

%T 2519775258000,8315258351400,716624083375200,33382738550561400,

%U 1114469886995665200,5970374394619635000,340709365452960504000,6878070315081640174500

%N Numerator of the harmonic mean of the first n 9-gonal numbers.

%H Colin Barker, <a href="/A250548/b250548.txt">Table of n, a(n) for n = 1..800</a>

%e a(3) = 216 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,pns},pns=PolygonalNumber[9,Range[nn]];Numerator[Table[ HarmonicMean[Take[pns,n]],{n,nn}]]] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Sep 30 2016 *)

%o (PARI)

%o harmonicmean(v) = #v / sum(k=1, #v, 1/v[k])

%o s=vector(30); for(n=1, #s, s[n]=numerator(harmonicmean(vector(n, k, (7*k^2-5*k)/2)))); s

%Y Cf. A001106 (9-gonal numbers), A250549 (denominators).

%K nonn,frac

%O 1,2

%A _Colin Barker_, Nov 25 2014