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%I #10 Aug 30 2021 10:24:24
%S 1,4,20,110,640,3870,24084,153306,993978,6544242,43652340,294469974,
%T 2006018748,13784115468,95444016984,665407010349,4667570034444,
%U 32922870719664,233389493503968,1662048903052380,11885333877149532
%N The 4th 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 1 -4*x +12*x^2 -30*x^3 +64*x^4 -118*x^5 +188*x^6 -258*x^7 +302*x^8 -298*x^9 +244*x^10 -162*x^11 +84*x^12 -32*x^13 +8*x^14 -x^15. - _R. J. Mathar_, Aug 30 2021
%o (PARI) {a(n)=local(F=serreverse(x-x^2+O(x^(n+1))),G=x); for(i=1,4,G=subst(F,x,G));polcoeff(G,n)}
%Y Cf. A158825, A158826, A158828, A158829.
%K nonn
%O 1,2
%A _Paul D. Hanna_, Mar 28 2009
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