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 A337825 #5 Sep 24 2020 13:59:59
%S A337825 0,1,6,-33,-512,19405,181116,-45817541,771776384,280415588121,
%T A337825 -23151651942500,-3217963989270569,816268626535923936,
%U A337825 38087192839910816485,-43268389662374707851552,2822720920753640236252875,3297662826737476255127428096,-833876355494162903256716734927
%N A337825 a(0) = 0; a(n) = n^3 - (1/n) * Sum_{k=1..n-1} binomial(n,k)^2 * (n-k)^3 * k * a(k).
%F A337825 Sum_{n>=0} a(n) * x^n / (n!)^2 = log(1 + x * (BesselI(0,2*sqrt(x)) + sqrt(x) * BesselI(1,2*sqrt(x)))).
%F A337825 Sum_{n>=0} a(n) * x^n / (n!)^2 = log(1 + Sum_{n>=1} n^3 * x^n / (n!)^2).
%t A337825 a[0] = 0; a[n_] := a[n] = n^3 - (1/n) * Sum[Binomial[n, k]^2 (n - k)^3 k a[k], {k, 1, n - 1}]; Table[a[n], {n, 0, 17}]
%t A337825 nmax = 17; CoefficientList[Series[Log[1 + x (BesselI[0, 2 Sqrt[x]] + Sqrt[x] BesselI[1, 2 Sqrt[x]])], {x, 0, nmax}], x] Range[0, nmax]!^2
%Y A337825 Cf. A002190, A101981, A300452, A337590, A337824, A337826.
%K A337825 sign
%O A337825 0,3
%A A337825 _Ilya Gutkovskiy_, Sep 24 2020