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A157675 G.f.: A(x) = exp( Sum_{n>=1} A(2^n*x)^n * x^n/n ). 4

%I

%S 1,1,3,19,237,5741,270857,25099497,4605241487,1681614043919,

%T 1225216121453227,1783355695990213771,5188617952349909215215,

%U 30183911091753947571225583,351131331387346570480797774119

%N G.f.: A(x) = exp( Sum_{n>=1} A(2^n*x)^n * x^n/n ).

%C Conjectured to consist entirely of integers.

%C Compare to: C(x) = exp( Sum_{n>=1} C(x)^n*x^n/n ) where C(x) = g.f. of Catalan numbers (A000108).

%e G.f.: A(x) = 1 + x + 3*x^2 + 19*x^3 + 237*x^4 + 5741*x^5 + 270857*x^6 +...

%e A(x) = exp(A(2x)*x + A(4x)^2*x^2/2 + A(8x)^3*x^3/3 + A(16x)^4*x^4/4 +...).

%o (PARI) {a(n)=local(A=1+x);for(i=1,n,A=exp(sum(m=1,n,subst(A,x,2^m*x +x*O(x^n))^m*x^m/m)));polcoeff(A,n)}

%Y Cf. A156907.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Mar 06 2009

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Last modified May 22 08:21 EDT 2022. Contains 353933 sequences. (Running on oeis4.)