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 A365031 #24 Dec 01 2024 10:51:40
%S A365031 1,1,7,70,1085,22176,569107,17583616,636085305,26383168000,
%T A365031 1234691104031,64368785424384,3699873561469813,232476344504965120,
%U A365031 15853643565560296875,1166213594266747273216,92052000392983157418353,7760655405804462332903424
%N A365031 E.g.f. satisfies A(x) = exp(x * A(x) * (1 + x * A(x))^2).
%H A365031 Michael De Vlieger, <a href="/A365031/b365031.txt">Table of n, a(n) for n = 0..352</a>
%H A365031 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A365031 a(n) = n! * Sum_{k=0..n} (n+1)^(k-1) * binomial(2*k,n-k)/k!.
%F A365031 E.g.f.: (1/x) * Series_Reversion( x*exp(-x*(1 + x)^2) ). - _Seiichi Manyama_, Sep 23 2024
%t A365031 Array[#!*Sum[ (# + 1)^(k - 1)*Binomial[2 k, # - k]/k!, {k, 0, #}] &, 18, 0] (* _Michael De Vlieger_, Aug 18 2023 *)
%o A365031 (PARI) a(n) = n!*sum(k=0, n, (n+1)^(k-1)*binomial(2*k, n-k)/k!);
%Y A365031 Cf. A088695, A365032.
%Y A365031 Cf. A364939.
%K A365031 nonn
%O A365031 0,3
%A A365031 _Seiichi Manyama_, Aug 17 2023