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 A384501 #4 May 31 2025 10:46:25
%S A384501 1,0,1,9,119,2025,42510,1062761,30854159,1020615912,37900765365,
%T A384501 1561459425955,70682817696436,3487456195458027,186281997929231659,
%U A384501 10709829446929099865,659427284782849503663,43293574636994934145044,3019108475859713906967738,222868205832269470083471366
%N A384501 a(n) = Sum_{k=0..n} abs(Stirling1(n,k)) * Stirling2(n,n-k).
%F A384501 a(n) = Sum_{k=0..n} abs(Stirling1(n,n-k)) * Stirling2(n,k).
%F A384501 a(n) ~ c * ((-r - 1/((1-r)*LambertW(exp(1/(r-1))/(r-1)))) / (1 + (1-r)*LambertW(exp(1/(r-1))/(r-1))))^n * n^(n - 1/2) / exp(n), where r = 0.412059483521755003540032983286575579547027818844750... is the root of the equation (1-r)^2 * (1 + LambertW(-1, -exp(-r)*r)/r) = (1-r) + 1/LambertW(exp(1/(r-1))/(r-1)) and c = 0.21367572159147979376975234273...
%t A384501 Table[Sum[Abs[StirlingS1[n, k]]*StirlingS2[n, n-k], {k, 0, n}], {n, 0, 20}]
%t A384501 Table[Sum[StirlingS2[n, k]*Abs[StirlingS1[n, n-k]], {k, 0, n}], {n, 0, 20}]
%Y A384501 Cf. A047793, A187655, A187656.
%K A384501 nonn
%O A384501 0,4
%A A384501 _Vaclav Kotesovec_, May 31 2025