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%I #7 Jan 08 2017 16:20:16
%S 1,1,3,21,171,1821,24123,373941,6652971,134043021,3015804123,
%T 74896835301,2035155307851,60060014359101,1912775342667003,
%U 65386505879278101,2387952288823631211,92787780103004673261,3822149820074294439963,166370252948982266633541,7630279185863896475367051
%N E.g.f. satisfies: A'(x) = Product_{n>=1} (1 + A(x)^n), where A(0) = 0.
%H Vaclav Kotesovec, <a href="/A233861/b233861.txt">Table of n, a(n) for n = 1..110</a>
%F E.g.f. satisfies: log(A'(x)) = Sum_{n>=1} A000593(n)*A(x)^n/n, where A000593(n) is the sum of odd divisors of n.
%F Contribution from _Paul D. Hanna_, Jan 08 2017: (Start)
%F E.g.f. A(x) satisfies:
%F (1) A(x) = Series_Reversion( Integral Product_{n>=1} 1/(1+x^n) dx ).
%F (2) A(x) = Integral Product_{n>=1} (1 + A(x)^n) dx.
%F (End)
%e E.g.f. A(x) = x + x^2/2! + 3*x^3/3! + 21*x^4/4! + 171*x^5/5! + 1821*x^6/6! +...
%e where
%e A'(x) = (1 + A(x)) * (1 + A(x)^2) * (1 + A(x)^3) * (1 + A(x)^4) * (1 + A(x)^5) *...
%o (PARI) {a(n)=local(A=x); for(i=1, n, A=intformal(prod(k=1,n,1+A^k+x*O(x^n)))); n!*polcoeff(A, n)}
%o for(n=1, 30, print1(a(n), ", "))
%Y Cf. A233860.
%K nonn
%O 1,3
%A _Paul D. Hanna_, Dec 16 2013
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