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 A385408 #12 Jun 27 2025 18:25:41
%S A385408 1,1,8,388,113480,199246816,2099255895008,132708276995157568,
%T A385408 50336523318422432038400,114556539064849604787867141376,
%U A385408 1564256035642651626332994903500876288,128158392280785912677966097933268099449960448,62999559569114394473388668602373642996554916532377600
%N A385408 Sum over all ordered partitions of [n] of 6^j for an ordered partition with j inversions.
%H A385408 Alois P. Heinz, <a href="/A385408/b385408.txt">Table of n, a(n) for n = 0..51</a>
%H A385408 Wikipedia, <a href="https://en.wikipedia.org/wiki/Inversion_(discrete_mathematics)">Inversion</a>
%H A385408 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%F A385408 a(n) = Sum_{k=0..binomial(n,2)} A381299(n,k)*6^k.
%p A385408 b:= proc(o, u, t) option remember; `if`(u+o=0, 1, `if`(t=1,
%p A385408 b(u+o, 0$2), 0)+add(6^(u+j-1)*b(o-j, u+j-1, 1), j=1..o))
%p A385408 end:
%p A385408 a:= n-> b(n, 0$2):
%p A385408 seq(a(n), n=0..14);
%Y A385408 Column k=6 of A381426.
%Y A385408 Cf. A000670, A381299.
%K A385408 nonn
%O A385408 0,3
%A A385408 _Alois P. Heinz_, Jun 27 2025