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%I #5 Sep 17 2023 21:26:59
%S 1,1,3,19,235,5611,261387,24036747,4393513739,1601446102795,
%T 1165813783355659,1696186361756285195,4933983374364840587531,
%U 28699669301301875112931595,333847943551999970556459225355,7766615964534009591489133873762571
%N G.f. satisfies: A(x) = Sum_{n>=0} x^n * Product_{k=1..n} A(2^k*x).
%e G.f.: A(x) = 1 + x + 3*x^2 + 19*x^3 + 235*x^4 + 5611*x^5 + 261387*x^6 + ...
%e where
%e A(x) = 1 + x*A(2*x) + x^2*A(2*x)*A(4*x) + x^3*A(2*x)*A(4*x)*A(8*x) + ...
%o (PARI) {a(n, r=1)=local(A=1+x); for(i=1, n, A=1+sum(m=1, n, r^m*x^m*prod(k=1, m, subst(A, x, 2^k*x+x*O(x^n))))); polcoeff(A, n)}
%o for(n=0,20,print1(a(n),", "))
%Y Cf. A158888, A178089.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Oct 15 2013
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