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 A347726 #17 Apr 12 2023 08:05:03
%S A347726 1,1,1,7,37,221,1801,15709,157641,1775521,21898801,296379931,
%T A347726 4346295757,68682481141,1163591541113,21024039322441,403559222086801,
%U A347726 8199021870113985,175746277620520417,3963144157484213359,93778090395227788021,2323080237693908254381
%N A347726 Expansion of e.g.f.: exp(x / (1-x)^x).
%F A347726 a(n) = n! * Sum_{i=0..n} (-1)^(n-i) * ( Sum_{j=0..n-i} i^j * Stirling1(n-i-j,j)/(n-i-j)! )/i!.
%t A347726 a[0] = 1; a[n_] := n! * Sum[(-1)^(n - i) * Sum[i^j * StirlingS1[n - i - j, j]/(n - i - j)!, {j, 0, n - i}]/i!, {i, 1, n}]; Array[a, 20, 0] (* _Amiram Eldar_, Sep 11 2021 *)
%o A347726 (PARI) a(n) = n!*sum(i=0, n, (-1)^(n-i)*sum(j=0, n-i, i^j*stirling(n-i-j, j, 1)/(n-i-j)!)/i!);
%o A347726 (PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(exp(x/(1-x)^x)))
%Y A347726 Cf. A007113, A202152.
%K A347726 nonn
%O A347726 0,4
%A A347726 _Seiichi Manyama_, Sep 11 2021