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 A379702 #10 Dec 30 2024 11:24:01
%S A379702 1,0,5,11,333,2829,78553,1360197,42149817,1123709129,40775629581,
%T A379702 1453036152897,62005204699045,2736440768515869,135913168259011809,
%U A379702 7106229274104610829,405068417020871464689,24398077807975709138193,1574189366334360310720405
%N A379702 Expansion of e.g.f. (1/x) * Series_Reversion( x * exp(x) / (1 + x*exp(3*x)) ).
%F A379702 a(n) = (n!/(n+1)) * Sum_{k=0..n} (2*n-3*k-1)^k * binomial(n+1,n-k)/k!.
%o A379702 (PARI) a(n) = n!*sum(k=0, n, (2*n-3*k-1)^k*binomial(n+1, n-k)/k!)/(n+1);
%Y A379702 Cf. A108919, A379701.
%Y A379702 Cf. A366233.
%K A379702 nonn
%O A379702 0,3
%A A379702 _Seiichi Manyama_, Dec 30 2024