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G.f. A(x) satisfies: A(x)^5 = A(x^5) + 5*x.
4

%I #7 Sep 01 2022 12:04:30

%S 1,1,-2,6,-21,80,-320,1326,-5637,24434,-107542,479196,-2157045,

%T 9792702,-44780606,206055346,-953305632,4431463863,-20686696920,

%U 96931500840,-455722378776,2149086843549,-10162544469252,48176923330632,-228913129263389,1089973058779915

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

%C Not the same as A106223 or A196345.

%e G.f.: A(x) = 1 + x - 2*x^2 + 6*x^3 - 21*x^4 + 80*x^5 - 320*x^6 + 1326*x^7 - 5637*x^8 + 24434*x^9 - 107542*x^10 + 479196*x^11 + ...

%e such that A(x)^5 = A(x^5) + 5*x, as illustrated by:

%e A(x)^5 = 1 + 5*x + x^5 - 2*x^10 + 6*x^15 - 21*x^20 + 80*x^25 - 320*x^30 + 1326*x^35 - 5637*x^40 + 24434*x^45 - 107542*x^50 + ...

%o (PARI) {a(n) = my(A=1+x); for(i=0,n\5,

%o A = (subst(A,x,x^5) + 5*x + x*O(x^(5*n)))^(1/5));

%o polcoeff(A,n)}

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

%Y Cf. A107092, A352704, A352705.

%K sign

%O 0,3

%A _Paul D. Hanna_, Mar 29 2022