A250551 Denominator of the harmonic mean of the first n positive 10-gonal numbers.

1, 11, 307, 8117, 139393, 982381, 4935773, 287319059, 1056494083, 39179109811, 1609331378051, 4835480422963, 33892787092141, 1798339013862173, 34201770221163407, 4176177999344899729, 4179324192635626369, 32062945622467289429, 2341997846273161559117

Offset: 1

Author

Colin Barker, Nov 25 2014

Keywords

• nonn
• frac
• easy

Comments

a(n+1) is, for n >= 0, also the numerator of the partial sums of the reciprocal of the positive decagonal numbers A001107(n+1) with the denominators A294515(n) (provided A294515(n) = A250550(n+1)/(n+1)). - Wolfdieter Lang, Nov 02 2017

Examples

			a(3) = 307 because the first 3 positive decagonal numbers A001107 are [1,10,27], and 3/(1/1+1/10+1/27) = 810/307.
		

Links

• Colin Barker, Table of n, a(n) for n = 1..850

Crossrefs

Cf. A001107 (10-gonal numbers), A250550 (numerators).

Programs

Mathematica

With[{s = Array[PolygonalNumber[10, #] &, 19]}, Denominator@ Array[HarmonicMean@ Take[s, #] &, Length@ s]] (* Michael De Vlieger, Nov 02 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, (8*k^2-6*k)/2)))); s

Formula

a(n) = denominator(r(n)) with the rationals r(n) = n/Sum_{k=1..n} A001107(n), n >= 1. See the name. - Wolfdieter Lang, Nov 02 2017