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%I #7 Sep 01 2022 12:01:18
%S 1,1,-3,13,-65,351,-1989,11650,-69900,427167,-2648438,16612947,
%T -105215448,671760933,-4318468134,27926126553,-181520036178,
%U 1185220461867,-7769787812787,51117085998498,-337373170647840,2233091755252871,-14819626692452231,98582852467595847
%N G.f. A(x) satisfies: A(x)^7 = A(x^7) + 7*x.
%C Not the same as A106227.
%e G.f.: A(x) = 1 + x - 3*x^2 + 13*x^3 - 65*x^4 + 351*x^5 - 1989*x^6 + 11650*x^7 - 69900*x^8 + 427167*x^9 - 2648438*x^10 + ...
%e such that A(x)^7 = A(x^7) + 7*x, as illustrated by:
%e A(x)^7 = 1 + 7*x + x^7 - 3*x^14 + 13*x^21 - 65*x^28 + 351*x^35 - 1989*x^42 + 11650*x^49 - 69900*x^56 + 427167*x^63 - 2648438*x^70 + ...
%o (PARI) {a(n) = my(A=1+x); for(i=1,n,
%o A = (subst(A,x,x^7) + 7*x + x*O(x^n))^(1/7));
%o polcoeff(A,n)}
%o for(n=0,30,print1(a(n),", "))
%Y Cf. A107092, A352706, A352703.
%K sign
%O 0,3
%A _Paul D. Hanna_, Mar 29 2022
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