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From Peter Bala, Jun 02 2024: (Start)
A(x) = 1/(1 + x)*F(x/(1 + x)^4), where F(x) = Sum_{n >= 0} A002294(n)*x^n.
A(x) = 1/(1 + x) + x*A(x)^5. (End)
nonn,easy
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Seiichi Manyama, <a href="/A349300/b349300.txt">Table of n, a(n) for n = 0..500</a>
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a(n) ~ sqrt(1 - 3*r) / (2 * 5^(3/4) * sqrt(2*Pi*(1+r)) * n^(3/2) * r^(n + 1/4)), where r = 0.136824361675510443450981569282313811786270109272790613523286... is the root of the equation 5^5 * r = 4^4 * (1+r)^4. - Vaclav Kotesovec, Nov 14 2021
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