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 A380081 #10 Jan 12 2025 07:54:39
%S A380081 1,1,2,7,36,245,2086,21357,255704,3507625,54258570,934600601,
%T A380081 17743468612,368146983789,8288468950958,201258635444245,
%U A380081 5243025162331056,145871455305823697,4316920830720239122,135408946029576741297,4487574630295937337500,156686063319198543135061
%N A380081 Expansion of e.g.f. (1/x) * Series_Reversion( x / (1 + 3*x*exp(x))^(1/3) ).
%F A380081 E.g.f. A(x) satisfies A(x) = ( 1 + 3*x*A(x)*exp(x*A(x)) )^(1/3).
%F A380081 a(n) = (n!/(n+1)) * Sum_{k=0..n} 3^k * k^(n-k) * binomial(n/3+1/3,k)/(n-k)!.
%o A380081 (PARI) a(n) = n!*sum(k=0, n, 3^k*k^(n-k)*binomial(n/3+1/3, k)/(n-k)!)/(n+1);
%Y A380081 Cf. A161633, A380080.
%Y A380081 Cf. A380051.
%K A380081 nonn
%O A380081 0,3
%A A380081 _Seiichi Manyama_, Jan 11 2025