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%I #9 Sep 24 2024 14:14:53
%S 1,0,0,6,24,120,3240,45360,584640,13668480,322963200,7224940800,
%T 201040963200,6254004556800,197219089267200,6845849673062400,
%U 260976932536320000,10410615332941824000,441056225586706329600,20015606466369626112000,955852013167308601344000,47944066629381635801088000
%N E.g.f. satisfies A(x) = exp( x^3*A(x)^3 / (1 - x*A(x)) ).
%H <a href="/index/Res#revert">Index entries for reversions of series</a>
%F E.g.f.: (1/x) * Series_Reversion( x*exp(-x^3 / (1 - x)) ).
%F a(n) = n! * Sum_{k=0..floor(n/3)} (n+1)^(k-1) * binomial(n-2*k-1,n-3*k)/k!.
%o (PARI) a(n) = n!*sum(k=0, n\3, (n+1)^(k-1)*binomial(n-2*k-1, n-3*k)/k!);
%Y Cf. A052873, A376474.
%Y Cf. A293049.
%K nonn
%O 0,4
%A _Seiichi Manyama_, Sep 24 2024