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 A335811 #4 Jun 26 2020 06:22:30
%S A335811 1,0,0,-6,-36,-270,-1620,-8526,-41076,-549870,-13520340,-262959246,
%T A335811 -3587233716,-22581847470,584571618540,30096769542834,859315925548044,
%U A335811 18434866643574930,285138881159407020,2045091797042889714,-28367019385288799796,379914681728984325330
%N A335811 E.g.f.: exp(x) * Product_{k>=1} (1 + (1 - exp(x))^k).
%C A335811 Stirling-Bernoulli transform of A000009.
%F A335811 a(n) = Sum_{k=0..n} (-1)^k * Stirling2(n+1,k+1) * k! * A000009(k).
%t A335811 nmax = 21; CoefficientList[Series[Exp[x] Product[(1 + (1 - Exp[x])^k), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
%t A335811 Table[Sum[(-1)^k StirlingS2[n + 1, k + 1] k! PartitionsQ[k], {k, 0, n}], {n, 0, 21}]
%Y A335811 Cf. A000009, A305550, A327601.
%K A335811 sign
%O A335811 0,4
%A A335811 _Ilya Gutkovskiy_, Jun 25 2020