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

1, 9, 197, 503, 6623, 17813, 340527, 3763087, 169947523, 170436583, 5295982873, 90208585541, 3343268872217, 3348036962687, 144143598106421, 1659445372263179, 11627213232841853, 3879029288899801, 352907045903771, 10241306344308349, 208368821623076563

Offset: 1

Author

Colin Barker, Nov 21 2014

Keywords

• nonn
• frac
• easy

Comments

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

Examples

			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.
		

Links

• Colin Barker, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000567 (octagonal numbers), A250400 (numerators), A294512.

Programs

Maple

f:= n -> denom(n/add(1/(k*(3*k-2)),k=1..n)):
map(f, [$1..40]); # Robert Israel, Nov 01 2017

Mathematica

With[{s = Array[PolygonalNumber[8, #] &, 21]}, Denominator@ Array[HarmonicMean@ Take[s, #] &, Length@ s]] (* Michael De Vlieger, Nov 01 2017 *)

PARI

harmonicmean(v) = #v / sum(k=1, #v, 1/v[k])
s=vector(30); for(n=1, #s, s[n]=denominator(harmonicmean(vector(n, k, 3*k^2-2*k)))); s

Formula

Denominator of 12*n/(Pi*sqrt(3) + 9*log(3) + 6*Psi(n+1/3) - 6*Psi(n+1)). - Robert Israel, Nov 01 2017