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 A341815 #5 Feb 20 2021 11:03:27
%S A341815 1,1,12,270,8960,406250,23293872,1617774592,132075970560,
%T A341815 12397121784954,1315528361642000,155743010418063860,
%U A341815 20351866171905066240,2909818652684404979440,451849287590990124662400,75730203998219999637000000,13625593688459657260608782336,2619521322904712777031960349850
%N A341815 a(n) = Sum_{k=0..n} binomial(n,k)^3 * k^n.
%C A341815 For m>0, Sum_{k=0..n} binomial(n,k)^m * k^n ~ c(m) * d^n * n! / n^(m/2), where d = (1 + m*LambertW(exp(-1/m)/m))^(m-1) / (m^m * LambertW(exp(-1/m)/m)^m) and c(m) is a constant independent of n.
%F A341815 a(n) ~ c * d^n * n! / n^(3/2), where d = (1 + 3*LambertW(exp(-1/3)/3))^2 / (27 * LambertW(exp(-1/3)/3)^3) = 12.3645613141726293982008517178673172577947617775... and c = 0.143687082995832067469009730530027989920523409582173778129054767279...
%t A341815 Join[{1}, Table[Sum[k^n * Binomial[n, k]^3, {k, 0, n}], {n, 1, 20}]]
%Y A341815 Cf. A072034, A336828.
%K A341815 nonn
%O A341815 0,3
%A A341815 _Vaclav Kotesovec_, Feb 20 2021