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A352704 G.f. A(x) satisfies: (1 - x*A(x))^5 = 1 - 5*x - x^5*A(x^5).

%I A352704 #9 Sep 01 2022 12:09:31
%S A352704 1,2,6,21,80,320,1326,5637,24434,107542,479196,2157045,9792702,
%T A352704 44780606,206055346,953305632,4431463863,20686696920,96931500840,
%U A352704 455722378776,2149086843549,10162544469252,48176923330632,228913129263389,1089973058779915,5199987220813564
%N A352704 G.f. A(x) satisfies: (1 - x*A(x))^5 = 1 - 5*x - x^5*A(x^5).
%C A352704 Essentially an unsigned version of A352703 (after dropping the initial term).
%H A352704 Paul D. Hanna, <a href="/A352704/b352704.txt">Table of n, a(n) for n = 0..1000</a>
%F A352704 G.f. A(x) satisfies:
%F A352704 (1) (1 + x*A(-x))^5 = 1 + 5*x + x^5*A(-x^5).
%F A352704 (2) A(x) = (1 - (1 - 5*x - x^5*A(x^5))^(1/5))/x.
%F A352704 (3) A(x)^5 = A(x^5) (mod 5).
%e A352704 G.f.: A(x) = 1 + 2*x + 6*x^2 + 21*x^3 + 80*x^4 + 320*x^5 + 1326*x^6 + 5637*x^7 + 24434*x^8 + 107542*x^9 + 479196*x^10 + ...
%e A352704 where
%e A352704 (1 - x*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 + ...
%e A352704 also
%e A352704 (1 - 5*x - x^5*A(x^5))^(1/5) = 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 + ...
%e A352704 which equals 1 - x*A(x).
%o A352704 (PARI) {a(n) = my(A=1+2*x); for(i=1,n,
%o A352704 A = (1 - (1 - 5*x - x^5*subst(A,x,x^5) + x*O(x^(n+1)))^(1/5))/x);
%o A352704 polcoeff(A,n)}
%o A352704 for(n=0,30,print1(a(n),", "))
%Y A352704 Cf. A352703, A352702, A352706.
%K A352704 nonn
%O A352704 0,2
%A A352704 _Paul D. Hanna_, Mar 29 2022