This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A120286 #9 May 02 2024 10:46:42 %S A120286 1,9,65,725,3899,28763,419017,864669,7981633,3586319,200763407, %T A120286 2649665993,34899471137,176508049513,356606957297,12234391348253, %U A120286 209672027529221,4012917216669239,15350275129353301,15443118015171841 %N A120286 Numerator of 1/n^2 + 2/(n-1)^2 + 3/(n-2)^2 +...+ (n-1)/2^2 + n. %C A120286 p^2 divides a(p-1) for prime p>2. p divides a(p-2) for prime p>3. %F A120286 a(n) = numerator[Sum[Sum[1/i^2,{i,1,k}],{k,1,n}]]. %t A120286 Numerator[Table[Sum[Sum[1/i^2,{i,1,k}],{k,1,n}],{n,1,30}]] %t A120286 Table[-EulerGamma + HarmonicNumber[1 + n, 2] + n*HarmonicNumber[1 + n, 2] - PolyGamma[0, 2 + n], {n, 1, 20}] // Numerator (* _Vaclav Kotesovec_, May 02 2024 *) %o A120286 (Python) %o A120286 from fractions import Fraction %o A120286 def A120286(n): return sum(Fraction(n-i+1,i**2) for i in range(1,n+1)).numerator # _Chai Wah Wu_, May 01 2024 %Y A120286 Cf. A027612, A001008, A007406, A007407, A370774 (denom.). %K A120286 frac,nonn %O A120286 1,2 %A A120286 _Alexander Adamchuk_, Jul 07 2006