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 A382039 #14 Mar 13 2025 09:52:02
%S A382039 1,1,10,147,3252,96165,3569778,159771717,8378589096,504057519945,
%T A382039 34227869887710,2589957885708369,216121694333055228,
%U A382039 19717935804239270013,1952741002119283320714,208629930642065967641805,23919711023929511941080912,2929406351866509691077727761
%N A382039 Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 - x*exp(3*x)) ).
%F A382039 E.g.f. A(x) satisfies A(x) = 1 + x*A(x)^2*exp(3*x*A(x)).
%F A382039 a(n) = (1/(n+1)) * Sum_{k=0..n} (3*k)^(n-k) * (n+k)!/(k! * (n-k)!).
%o A382039 (PARI) a(n) = sum(k=0, n, (3*k)^(n-k)*(n+k)!/(k!*(n-k)!))/(n+1);
%Y A382039 Cf. A213644, A379690, A382040.
%Y A382039 Cf. A366233.
%K A382039 nonn
%O A382039 0,3
%A A382039 _Seiichi Manyama_, Mar 13 2025