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%I #3 Nov 27 2014 17:01:39
%S 1,1,4,40,485,6585,95732,1457636,22947585,370494965,6101028934,
%T 102074877086,1730213141683,29649526507055,512810063004600,
%U 8940267160930408,156944360941491106,2771866193105829798,49218079130561578390,878107603236732844610,15733529061871743649380
%N G.f. A(x) satisfies: 1+x = 2*A(x)^3 - A(x)^5.
%F G.f.: 1 + Series_Reversion(x - 4*x^2 - 8*x^3 - 5*x^4 - x^5).
%e G.f.: A(x) = 1 + x + 4*x^2 + 40*x^3 + 485*x^4 + 6585*x^5 + 95732*x^6 +...
%e Related expansions.
%e A(x)^3 = 1 + 3*x + 15*x^2 + 145*x^3 + 1755*x^4 + 23793*x^5 +...
%e A(x)^5 = 1 + 5*x + 30*x^2 + 290*x^3 + 3510*x^4 + 47586*x^5 +...
%e where 1+x = 2*A(x)^3 - A(x)^5.
%o (PARI) /* From 1+x = 2*A(x)^3 - A(x)^5: */
%o {a(n)=local(A=[1, 1]); for(i=1, n, A=concat(A, 0); A[#A]=-Vec(2*Ser(A)^3-Ser(A)^5)[#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 - 4*x^2 - 8*x^3 - 5*x^4 - x^5 + x^2*O(x^n)));polcoeff(A,n)}
%o for(n=0, 25, print1(a(n) , ", "))
%Y Cf. A249926, A249928, A249929, A249930, A249931, A249932.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Nov 27 2014
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