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G.f. A(x) satisfies: 1+x = 2*A(x)^4 - A(x)^7.
6

%I #7 Feb 07 2025 14:40:42

%S 1,1,9,189,4893,141771,4399549,143008579,4806584226,165685071354,

%T 5825261477574,208089042731934,7531002619598458,275548081670765638,

%U 10175724606458649366,378783118623851279250,14197727780171976218883,535401733845392629890255,20298674469757725391376887

%N G.f. A(x) satisfies: 1+x = 2*A(x)^4 - A(x)^7.

%F G.f.: 1 + Series_Reversion(x - 9*x^2 - 27*x^3 - 33*x^4 - 21*x^5 - 7*x^6 - x^7).

%e G.f.: A(x) = 1 + x + 9*x^2 + 189*x^3 + 4893*x^4 + 141771*x^5 +...

%e Related expansions.

%e A(x)^4 = 1 + 4*x + 42*x^2 + 868*x^3 + 22435*x^4 + 649488*x^5 +...

%e A(x)^7 = 1 + 7*x + 84*x^2 + 1736*x^3 + 44870*x^4 + 1298976*x^5 +...

%e where 1+x = 2*A(x)^4 - A(x)^7.

%o (PARI) /* From 1+x = 2*A(x)^4 - A(x)^7: */

%o {a(n)=local(A=[1, 1]); for(i=1, n, A=concat(A, 0); A[#A]=-Vec(2*Ser(A)^4-Ser(A)^7)[#A]); A[n+1]}

%o for(n=0, 25, print1(a(n) , ", "))

%o (PARI) /* From Series Reversion: */

%o {a(n)=local(A=1+serreverse(x - 9*x^2 - 27*x^3 - 33*x^4 - 21*x^5 - 7*x^6 - x^7 + x^2*O(x^n)));polcoeff(A,n)}

%o for(n=0, 25, print1(a(n) , ", "))

%Y Cf. A249926, A249927, A249928, A249929, A249930, A249931.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Nov 27 2014