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%I #9 Aug 30 2021 10:24:32
%S 1,5,30,195,1330,9380,67844,500619,3755156,28558484,219767968,
%T 1708590960,13403300208,105983648060,844009565176,6764300053390,
%U 54525119251104,441811163402124,3597005618194848,29412560840221272
%N The 5th iteration of x*C(x) where C(x) is the Catalan function (A000108).
%H Elżbieta Liszewska, Wojciech Młotkowski, <a href="https://arxiv.org/abs/1907.10725">Some relatives of the Catalan sequence</a>, arXiv:1907.10725 [math.CO], 2019.
%F Series reversion of x -5*x^2 +20*x^3 -70*x^4 +220*x^5 -630*x^6 +1656*x^7 -4014*x^8 +8994*x^9 -18654*x^10 +35832*x^11 -63750*x^12 +105024*x^13 -160120*x^14 +225696*x^15 -293685*x^16 +352074*x^17 -387820*x^18 +391232*x^19 -359992*x^20 +300664*x^21 -226580*x^22 +152952*x^23 -91656*x^24 +48204*x^25 -21924*x^26 +8456*x^27 -2692*x^28 +680*x^29 -128*x^30 +16*x^31 -x^32. - _R. J. Mathar_, Aug 30 2021
%o (PARI) {a(n)=local(F=serreverse(x-x^2+O(x^(n+1))),G=x); for(i=1,5,G=subst(F,x,G));polcoeff(G,n)}
%Y Cf. A158825, A158826, A158827, A158829.
%K nonn
%O 1,2
%A _Paul D. Hanna_, Mar 28 2009
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