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A250401 Denominator of the harmonic mean of the first n nonzero octagonal numbers.

%I A250401 #19 Nov 06 2017 04:58:27
%S A250401 1,9,197,503,6623,17813,340527,3763087,169947523,170436583,5295982873,
%T A250401 90208585541,3343268872217,3348036962687,144143598106421,
%U A250401 1659445372263179,11627213232841853,3879029288899801,352907045903771,10241306344308349,208368821623076563
%N A250401 Denominator of the harmonic mean of the first n nonzero octagonal numbers.
%C A250401 a(n+1), for n >= 0, is also the numerator of the partial sums of the reciprocal octagonal numbers Sum_{k=0..n} 1/((k + 1)*(3*k + 1)) with the denominators given in A294512(n) [assuming that n+1 divides A250400(n+1) to give A294512(n) for n >= 0]. - _Wolfdieter Lang_, Nov 01 2017
%H A250401 Colin Barker, <a href="/A250401/b250401.txt">Table of n, a(n) for n = 1..1000</a>
%F A250401 Denominator of 12*n/(Pi*sqrt(3) + 9*log(3) + 6*Psi(n+1/3) - 6*Psi(n+1)). - _Robert Israel_, Nov 01 2017
%e A250401 a(3) = 197 because the octagonal numbers A000567(n), for n = 1..3, are [1,8,21], and 3/(1/1 + 1/8 + 1/21) = 504/197.
%p A250401 f:= n -> denom(n/add(1/(k*(3*k-2)),k=1..n)):
%p A250401 map(f, [$1..40]); # _Robert Israel_, Nov 01 2017
%t A250401 With[{s = Array[PolygonalNumber[8, #] &, 21]}, Denominator@ Array[HarmonicMean@ Take[s, #] &, Length@ s]] (* _Michael De Vlieger_, Nov 01 2017 *)
%o A250401 (PARI)
%o A250401 harmonicmean(v) = #v / sum(k=1, #v, 1/v[k])
%o A250401 s=vector(30); for(n=1, #s, s[n]=denominator(harmonicmean(vector(n, k, 3*k^2-2*k)))); s
%Y A250401 Cf. A000567 (octagonal numbers), A250400 (numerators), A294512.
%K A250401 nonn,frac,easy
%O A250401 1,2
%A A250401 _Colin Barker_, Nov 21 2014