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A382016 E.g.f. A(x) satisfies A(x) = exp(x*B(x*A(x))), where B(x) = 1 + x*B(x)^4 is the g.f. of A002293.

%I A382016 #11 Mar 12 2025 09:39:04
%S A382016 1,1,3,37,901,32141,1502701,86737645,5952271977,473117681881,
%T A382016 42731313784921,4321503662185601,483709266378568429,
%U A382016 59360036142346311685,7924411424305558028757,1143251381667547987358581,177245340974472998607370321,29386977237154379581209716657
%N A382016 E.g.f. A(x) satisfies A(x) = exp(x*B(x*A(x))), where B(x) = 1 + x*B(x)^4 is the g.f. of A002293.
%F A382016 a(n) = n! * Sum_{k=0..n-1} (k+1)^(n-k-1) * binomial(n+3*k,k)/((n+3*k) * (n-k-1)!) for n > 0.
%o A382016 (PARI) a(n) = if(n==0, 1, n!*sum(k=0, n-1, (k+1)^(n-k-1)*binomial(n+3*k, k)/((n+3*k)*(n-k-1)!)));
%Y A382016 Cf. A161629, A161630, A382015.
%Y A382016 Cf. A002293, A380513.
%K A382016 nonn
%O A382016 0,3
%A A382016 _Seiichi Manyama_, Mar 12 2025