A250327 Numerator of the harmonic mean of the first n pentagonal numbers.

1, 5, 180, 2640, 23100, 157080, 183260, 2408560, 317026710, 10215305100, 89894684880, 19613385792, 403708857552, 17825298787296, 8681152006800, 435215087274240, 2312080151144400, 43249499297877600, 45652249258870800, 2835244953971976000, 4394629678656562800

Offset: 1

Author

Colin Barker, Nov 18 2014

Keywords

• nonn

Examples

			a(3) = 180 because the first 3 pentagonal numbers are [1,5,12] and 3/(1/1+1/5+1/12) = 180/77.
		

Links

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

Crossrefs

Cf. A250328 (denominators).

Programs

Mathematica

Table[Numerator[n/Total[1/PolygonalNumber[5,Range[n]]]],{n,30}] (* Harvey P. Dale, Jun 01 2022 *)

PARI

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