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%I #5 May 21 2017 07:49:01
%S 1,7,301,32347,6476281,2080072687,978357441061,633671918506627,
%T 540647648053353841,587611403828850167767,792504001599034713809821,
%U 1298643416767164198145121707,2541154725546790383213482500201,5852376595008692595588309106586047,15669400182952350735653156519506572181,48261540873448422135971738449165162450387,169430327422451431526680101559949211638388961
%N E.g.f. S(x) satisfies: S(x) = Integral (1 + S(x)^2)^(7/2) dx.
%F C(x)^2 - S(x)^2 = 1 and S'(x) = C(x)^7, where C(x) is described by A281436.
%o (PARI) {a(n) = my(S=x, C=1); for(i=1, n, S = intformal( C^7 +x*O(x^(2*n))); C = 1 + intformal( S*C^6 ) ); (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