A241997 - OEIS

%I #9 Aug 11 2014 06:34:59

%S 1,1,4,62,1530,50849,2089719,101470053,5660430287,355970992756,

%T 24894562936569,1915987357589537,160941576221849622,

%U 14653841416756810665,1437868649635368258342,151284341822917527109841,16993002921809143802858179,2029842747191877113876104045

%N G.f. satisfies: A(x)^2 = x + A(x*A(x)^5).

%H Vaclav Kotesovec, <a href="/A241997/b241997.txt">Table of n, a(n) for n = 0..250</a>

%F a(n) ~ c * 5^n * n^(n - 1/5 + 1/5*log(2)) / (exp(n) * log(2)^n), where c = 0.2007164067804229...

%o (PARI) {a(n)=local(A=[1, 1], Ax); for(i=1, n, A=concat(A, 0); Ax=Ser(A);

%o A[#A]=Vec(1+subst(Ax, x, x*Ax^5) - Ax^2)[#A]); A[n+1]}

%o for(n=0, 30, print1(a(n), ", "))

%Y Cf. A240996 (q=2), A240999 (q=3), A241996 (q=4), A241998 (q=6), A241999 (q=7).

%K nonn

%O 0,3

%A _Vaclav Kotesovec_, Aug 11 2014