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 A365013 #13 Aug 19 2023 06:28:58
%S A365013 1,1,5,58,1061,26536,843457,32553424,1478813513,77304347776,
%T A365013 4571222616701,301696674682624,21985118975444077,1753288356936334336,
%U A365013 151887264799071753785,14203597499192539334656,1426051485043745729079953,153000280727938469281693696
%N A365013 E.g.f. satisfies A(x) = exp( x*A(x)/(1 - x * A(x)^3) ).
%H A365013 Michael De Vlieger, <a href="/A365013/b365013.txt">Table of n, a(n) for n = 0..341</a>
%F A365013 a(n) = n! * Sum_{k=0..n} (3*n-2*k+1)^(k-1) * binomial(n-1,n-k)/k!.
%t A365013 Array[#!*Sum[ (3 # - 2 k + 1)^(k - 1)*Binomial[# - 1, # - k]/k!, {k, 0, #}] &, 18, 0] (* _Michael De Vlieger_, Aug 18 2023 *)
%o A365013 (PARI) a(n) = n!*sum(k=0, n, (3*n-2*k+1)^(k-1)*binomial(n-1, n-k)/k!);
%Y A365013 Cf. A052873, A365012.
%K A365013 nonn
%O A365013 0,3
%A A365013 _Seiichi Manyama_, Aug 15 2023