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

1,2

Links

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

Example

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A250328 (denominators).

Sequence in context: A136143 A035791 A324090 * A366342 A162136 A053363

Adjacent sequences: A250324 A250325 A250326 * A250328 A250329 A250330

Keyword

nonn

Author

Colin Barker, Nov 18 2014

Status

approved