%I #11 Mar 06 2024 07:59:57
%S 1,1,4,30,360,5880,120960,2996280,86889600,2889976320,108501724800,
%T 4539844108800,209497816281600,10570762445443200,578997352591257600,
%U 34214810278128480000,2169772724008976486400,146984464202544531763200
%N Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 - x*exp(x^3)) ).
%H <a href="/index/Res#revert">Index entries for reversions of series</a>
%F a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} (n-3*k)^k * (2*n-3*k)!/(k! * (n-3*k)!).
%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1-x*exp(x^3)))/x))
%o (PARI) a(n) = sum(k=0, n\3, (n-3*k)^k*(2*n-3*k)!/(k!*(n-3*k)!))/(n+1);
%Y Cf. A213644, A370927.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Mar 06 2024
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