A250550 Numerator of the harmonic mean of the first n 10-gonal numbers.

1, 20, 810, 28080, 596700, 5012280, 29238300, 1938081600, 7994586600, 328666338000, 14822851843800, 48511151488800, 367876232123400, 20997243402735600, 427443883555689000, 55624697380046995200, 59101240966299932400, 479763014902905333600

Offset

1,2

Links

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

Example

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

Mathematica

Module[{nn=20, pn}, pns=PolygonalNumber[10, Range[nn]]; Table[HarmonicMean[ Take[ pns, n]], {n, nn}]]//Numerator (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Nov 09 2017 *)

Prog

(PARI)
harmonicmean(v) = #v / sum(k=1, #v, 1/v[k])
s=vector(30); for(n=1, #s, s[n]=numerator(harmonicmean(vector(n, k, (8*k^2-6*k)/2)))); s

Crossrefs

Cf. A001107 (10-gonal numbers), A250551 (denominators).

Sequence in context: A281777 A041763 A041760 * A292417 A117798 A006424

Adjacent sequences: A250547 A250548 A250549 * A250551 A250552 A250553

Keyword

nonn,frac

Author

Colin Barker, Nov 25 2014

Status

approved