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G.f. satisfies A(x) = 1 + x*A(x)*A(x^2)*A(x^3)*...*A(x^n)*...
10

%I #10 Nov 05 2021 04:17:14

%S 1,1,1,2,4,8,15,30,57,111,214,415,798,1547,2983,5765,11132,21510,

%T 41528,80231,154940,299280,578017,1116450,2156280,4164827,8044023,

%U 15536655,30007988,57958900,111943844,216213363,417602892,806575889,1557852990

%N G.f. satisfies A(x) = 1 + x*A(x)*A(x^2)*A(x^3)*...*A(x^n)*...

%H Vaclav Kotesovec, <a href="/A091865/b091865.txt">Table of n, a(n) for n = 0..210</a>

%F G.f.: A(x) = 1 + x * Product_{k>=1} A(x^k).

%F a(n) ~ c * d^n, where d = 1.93144101206639993844275031844664... and c = 0.29686384114142059645291926346897... - _Vaclav Kotesovec_, Oct 02 2020

%o (PARI) {a(n)=local(A);A=1+x;for(i=1,n, A=1+x*prod(k=1,n,subst(A,x,x^k))+x*O(x^n)); polcoeff(A,n,x)}

%Y Cf. A050383.

%K nonn

%O 0,4

%A _Paul D. Hanna_, Feb 05 2004