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%I #7 Nov 28 2017 03:48:29
%S 1,4,20,280,4660,86728,1727880,36047280,777470580,17195957480,
%T 387906427480,8890184148560,206419640698440,4845319424269520,
%U 114791477960006800,2741248077305459040,65915164046356799220
%N G.f. satisfies: 13*A(x) = 12 + 32*x + A(x)^5, starting with [1,4,20].
%C See comments in A120588 for conditions needed for an integer sequence to satisfy a functional equation of the form: r*A(x) = c + b*x + A(x)^n.
%F G.f.: A(x) = 1 + Series_Reversion((1+13*x - (1+x)^5)/32). Lagrange Inversion yields: G.f.: A(x) = Sum_{n>=0} C(5*n,n)/(4*n+1) * (12+32*x)^(4*n+1)/13^(5*n+1). - _Paul D. Hanna_, Jan 24 2008
%F a(n) ~ 2^(-3/2 + 5*n) * (-12 + 4*(13/5)^(5/4))^(1/2 - n) / (5^(1/8) * 13^(3/8) * n^(3/2) * sqrt(Pi)). - _Vaclav Kotesovec_, Nov 28 2017
%e A(x) = 1 + 4*x + 20*x^2 + 280*x^3 + 4660*x^4 + 86728*x^5 +...
%e A(x)^5 = 1 + 20*x + 260*x^2 + 3640*x^3 + 60580*x^4 + 1127464*x^5 +...
%t CoefficientList[1 + InverseSeries[Series[(1+13*x - (1+x)^5)/32, {x, 0, 20}], x], x] (* _Vaclav Kotesovec_, Nov 28 2017 *)
%o (PARI) {a(n)=local(A=1+4*x+20*x^2+x*O(x^n));for(i=0,n,A=A+(-13*A+12+32*x+A^5)/8);polcoeff(A,n)}
%Y Cf. A120588 - A120598, A120600 - A120607.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Jun 16 2006
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