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 A351769 #18 Jun 02 2022 15:38:20
%S A351769 1,1,17,827,79368,12623124,3002832110,998401869464,442148442609152,
%T A351769 251578963946182968,178846127724854653704,155339277405600252114072,
%U A351769 161863497852092601156187152,199286757107586767535516731832,286210094619439661737214469710088
%N A351769 a(n) = Sum_{k=0..n} (-1)^(n-k) * Stirling1(n, k) * k^(k+n).
%H A351769 Seiichi Manyama, <a href="/A351769/b351769.txt">Table of n, a(n) for n = 0..213</a>
%F A351769 a(n) ~ c * r^n * (1 + r*exp(1 + 1/r))^n * n^(2*n) / exp(2*n), where r = 0.937997555632908331545534056235449048849427140626270261830822459734975609... is the root of the equation r + exp(-1 - 1/r) = -LambertW(-1, -r*exp(-r)) and c = 0.9367460233410089838603007174937882495902299959682250862650092226619624... - _Vaclav Kotesovec_, Feb 18 2022
%F A351769 E.g.f.: Sum_{k>=0} (-k * log(1 - k*x))^k / k!. - _Seiichi Manyama_, Jun 02 2022
%t A351769 Table[Sum[k^(k+n) * StirlingS1[n, k] * (-1)^(n-k), {k, 0, n}], {n, 0, 20}]
%o A351769 (PARI) a(n) = sum(k=0, n, (-1)^(n-k)*stirling(n, k, 1)*k^(k+n)); \\ _Michel Marcus_, Feb 19 2022
%o A351769 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (-k*log(1-k*x))^k/k!))) \\ _Seiichi Manyama_, Jun 02 2022
%Y A351769 Cf. A351180, A351181.
%K A351769 nonn
%O A351769 0,3
%A A351769 _Vaclav Kotesovec_, Feb 18 2022