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 A331661 #4 Jan 24 2020 20:57:21
%S A331661 1,1,-3,6,30,-720,9180,-79020,-283500,41886720,-1580008680,
%T A331661 44344341000,-851982076440,-5914076263200,1972181136416400,
%U A331661 -153108297672649200,8900721288190544400,-403768420629168268800,9341444542413659205600,856476985107522346596000
%N A331661 E.g.f. A(x) satisfies: d/dx A(x) = 1 + (1/(1 + x)) * A(x/(1 + x)).
%F A331661 a(1) = 1; a(n+1) = Sum_{k=0..n-1} (-1)^k * binomial(n,k)^2 * k! * a(n-k).
%t A331661 terms = 20; A[_] = 0; Do[A[x_] = Normal[Integrate[1 + 1/(1 + x) A[x/(1 + x) + O[x]^(terms + 1)], x] + O[x]^(terms + 1)], terms]; CoefficientList[A[x], x] Range[0, terms]! // Rest
%t A331661 a[1] = 1; a[n_] := a[n] = Sum[(-1)^k Binomial[n - 1, k]^2 k! a[n - k - 1], {k, 0, n - 2}]; Table[a[n], {n, 1, 20}]
%Y A331661 Cf. A307355, A331660.
%K A331661 sign
%O A331661 1,3
%A A331661 _Ilya Gutkovskiy_, Jan 23 2020