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 A330604 #7 Dec 19 2019 16:47:22
%S A330604 1,0,9,278,16145,1471774,194652577,35275961958,8397548586177,
%T A330604 2542220603893358,954003495852753401,434683708245705663766,
%U A330604 236409592518584290327249,151286889086525353482149022,112534788142976814403622739921,96285847680519841273313314779974
%N A330604 a(n) = Sum_{k>=0} (n*k - 1)^n / 2^(k + 1).
%F A330604 a(n) = n! * [x^n] exp(-x) / (2 - exp(n*x)).
%F A330604 a(n) = Sum_{k=0..n} (-1)^(n - k) * binomial(n,k) * n^k * A000670(k).
%F A330604 a(n) ~ n^n * n! / (2 * (log(2))^(n+1)). - _Vaclav Kotesovec_, Dec 19 2019
%t A330604 Table[Sum[(n k - 1)^n/2^(k + 1), {k, 0, Infinity}], {n, 0, 15}]
%t A330604 Join[{1}, Table[n^n HurwitzLerchPhi[1/2, -n, -1/n]/2, {n, 1, 15}]]
%t A330604 Table[n! SeriesCoefficient[Exp[-x]/(2 - Exp[n x]), {x, 0, n}], {n, 0, 15}]
%Y A330604 Cf. A000670, A052841, A308864, A330605.
%K A330604 nonn
%O A330604 0,3
%A A330604 _Ilya Gutkovskiy_, Dec 19 2019