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%I #3 Jun 06 2012 19:49:14
%S 1,1,2,8,35,181,1042,6301,39435,249744,1585386,10027385,62696192,
%T 385398251,2322152120,13727653882,80274175978,472701550856,
%U 2883417403654,18796497074750,132728456810968,995480740265410,7605881152587204,56821415293287735,403362682583930224
%N G.f. satisfies: A(x) = 1/(1 - x/A(-x*A(x)^6)).
%C Compare g.f. to:
%C (1) G(x) = 1/(1 - x/G(-x*G(x)^3)^1) when G(x) = 1/(1 - x*G(x)^1) (A000108).
%C (2) G(x) = 1/(1 - x/G(-x*G(x)^5)^2) when G(x) = 1/(1 - x*G(x)^2) (A001764).
%C (3) G(x) = 1/(1 - x/G(-x*G(x)^7)^3) when G(x) = 1/(1 - x*G(x)^3) (A002293).
%C (4) G(x) = 1/(1 - x/G(-x*G(x)^9)^4) when G(x) = 1/(1 - x*G(x)^4) (A002294).
%e G.f.: A(x) = 1 + x + 2*x^2 + 8*x^3 + 35*x^4 + 181*x^5 + 1042*x^6 +...
%e Related expansions:
%e A(x)^6 = 1 + 6*x + 27*x^2 + 128*x^3 + 645*x^4 + 3462*x^5 + 19823*x^6 +...
%e 1/A(-x*A(x)^6) = 1 + x + 5*x^2 + 20*x^3 + 108*x^4 + 638*x^5 + 3889*x^6 +...
%o (PARI) {a(n)=local(A=1+x+x*O(x^n)); for(i=1, n, A=1/(1-x/subst(A, x, -x*subst(A^6, x, x+x*O(x^n)))) ); polcoeff(A, n)}
%o for(n=0, 30, print1(a(n), ", "))
%Y Cf. A213225, A213226, A213228, A213229, A213230, A213231, A213232, A213233.
%Y Cf. A213091, A213092, A213093, A213094, A213095, A213096, A213098.
%Y Cf. A213099, A213100, A213101, A213102, A213103, A213104, A213105.
%Y Cf. A213108, A213109, A213110, A213111, A213112, A213113.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Jun 06 2012
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