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 A336259 #12 Jan 04 2024 19:11:08
%S A336259 1,1,9,278,20464,2948824,735078968,291153023664,172201253334528,
%T A336259 145044581320046592,167609226267379703808,257816558769660828601344,
%U A336259 514890814087717253133447168,1307445058678686737908660752384,4146656933568759002389401276616704
%N A336259 a(0) = 1; a(n) = (n!)^3 * Sum_{k=0..n-1} a(k) / (k! * (n-k))^3.
%H A336259 Alois P. Heinz, <a href="/A336259/b336259.txt">Table of n, a(n) for n = 0..180</a>
%F A336259 a(n) = (n!)^3 * [x^n] 1 / (1 - polylog(3,x)).
%F A336259 a(n) ~ (n!)^3 / (polylog(2,r) * r^n), where r = 0.86512013798076629268795131756... is the root of the equation polylog(3,r) = 1. - _Vaclav Kotesovec_, Jul 15 2020
%p A336259 b:= proc(n) option remember; `if`(n=0, 1,
%p A336259 add(b(n-i)/i^3, i=1..n))
%p A336259 end:
%p A336259 a:= n-> n!^3*b(n):
%p A336259 seq(a(n), n=0..14); # _Alois P. Heinz_, Jan 04 2024
%t A336259 a[0] = 1; a[n_] := a[n] = (n!)^3 Sum[a[k]/(k! (n - k))^3, {k, 0, n - 1}]; Table[a[n], {n, 0, 14}]
%t A336259 nmax = 14; CoefficientList[Series[1/(1 - PolyLog[3, x]), {x, 0, nmax}], x] Range[0, nmax]!^3
%Y A336259 Cf. A007840, A193436, A336195, A336258, A336260, A336261.
%K A336259 nonn
%O A336259 0,3
%A A336259 _Ilya Gutkovskiy_, Jul 15 2020