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 A330895 #23 May 09 2020 03:36:26
%S A330895 0,0,0,2,29,46,3049,60574,160599,182789,4913659,1072364,975570703,
%T A330895 1039388677,5491155875,92211937094,6954047816459,7225392149719,
%U A330895 2699717387790739,2785123121790325,573031978700759,84009502802237,45510401082365873,46518885869845328
%N A330895 Numerator of the variance of the random number of comparisons in quicksort applied to lists of length n.
%D A330895 D. E. Knuth, The Art of Computer Programming, Volume 3: Sorting and Searching, Addison-Wesley, 1973; see answer to Ex. 8(a) of Section 6.2.2.
%H A330895 S. B. Ekhad and D. Zeilberger, <a href="https://arxiv.org/abs/1903.03708">A detailed analysis of quicksort running time</a>, arXiv:1903.03708 [math.PR], 2019; see Theorem 2.
%H A330895 V. Iliopoulos, <a href="https://arxiv.org/abs/1503.02504">The quicksort algorithm and related topics</a>, arXiv:1503.02504 [cs.DS], 2015.
%H A330895 V. Iliopoulos and D. Penman, <a href="https://arxiv.org/abs/1006.4063">Variance of the number of comparisons of randomized quicksort</a>, arXiv:1006.4063 [math.PR], 2010.
%F A330895 a(n) = numerator(fr(n)), where fr(n) = n*(7*n + 13) - 2*(n + 1)*Sum_{k=1..n} 1/k - 4*(n + 1)^2*Sum_{k=1..n} 1/k^2.
%e A330895 The variances are: 0, 0, 0, 2/9, 29/36, 46/25, 3049/900, 60574/11025, 160599/19600, 182789/15876, 4913659/317520, 1072364/53361, ... = A330895/A330907.
%o A330895 (PARI) lista(nn) = {my(va = vector(nn)); for(n=1, nn, va[n] = numerator(n*(7*n+13) - 2*(n+1)*sum(k=1, n, 1/k) - 4*(n+1)^2*sum(k=1, n, 1/k^2))); concat(0,va);}
%Y A330895 Cf. A063090, A067699, A093418, A096620, A115107, A288964, A288965, A288970, A288971, A329001, A330852, A330860, A330875, A330876, A330907 (denominators).
%K A330895 nonn,frac
%O A330895 0,4
%A A330895 _Petros Hadjicostas_, May 01 2020