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E.g.f. S(x) satisfies: S(x) = Integral (1 + S(x)^2)^(9/2) dx.
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%I #5 May 21 2017 07:49:22

%S 1,9,513,73737,19832769,8579840841,5445003346497,4764370917991113,

%T 5496694973220383361,8084246464894865788809,

%U 14762694711793154790084993,32769963553535754858524377737,86898373859771331049009442719809,271302297590897772500098532033111241,985007641595004757219829801609866106817,4114936376199336730220297730026151662954313,19598505312024077134206058809303825114147365121

%N E.g.f. S(x) satisfies: S(x) = Integral (1 + S(x)^2)^(9/2) dx.

%F C(x)^2 - S(x)^2 = 1 and S'(x) = C(x)^9, where C(x) is described by A281444.

%o (PARI) {a(n) = my(S=x, C=1); for(i=1, n, S = intformal( C^9 +x*O(x^(2*n))); C = 1 + intformal( S*C^8 ) ); (2*n-1)!*polcoeff(S, 2*n-1)}

%o for(n=1, 30, print1(a(n), ", "))

%K nonn

%O 1,2

%A _Paul D. Hanna_, Jan 21 2017