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E.g.f. satisfies: A(x) = exp(x*A(3*x)^(1/3)).
1

%I #9 Aug 25 2024 17:00:51

%S 1,1,3,28,941,121696,58279927,98693039488,574767759680921,

%T 11307939591431088640,741800547536454112053131,

%U 160601295262890881800391317504,113798222852671185437521059198500869,262065699673092152689287590716544261804032

%N E.g.f. satisfies: A(x) = exp(x*A(3*x)^(1/3)).

%e E.g.f.: A(x) = 1 + x + 3*x^2/2! + 28*x^3/3! + 941*x^4/4! + 121696*x^5/5! +...

%e where

%e A(3*x)^(1/3) = 1 + x + 7*x^2/2! + 208*x^3/3! + 23365*x^4/4! + 9588976*x^5/5! +...

%o (PARI) {a(n)=local(A=1+x);for(i=1,21,A=exp(x*subst(A,x,3*x+x*O(x^n))^(1/3)));n!*polcoeff(A,n)}

%Y Cf. A196734.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Oct 05 2011