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%I #3 Nov 27 2014 17:04:01
%S 1,1,4,42,530,7489,113289,1794784,29397876,493818165,8460325159,
%T 147264321834,2596986868762,46299572773077,833111268412360,
%U 15110637698827976,275970530427257207,5070759797283817869,93671715612197557390,1738657226550598494420,32409645286487921390715
%N G.f. A(x) satisfies: 1+x = A(x)^2 + A(x)^5 - A(x)^6.
%F G.f.: 1 + Series_Reversion(x - 4*x^2 - 10*x^3 - 10*x^4 - 5*x^5 - x^6).
%e G.f.: A(x) = 1 + x + 4*x^2 + 42*x^3 + 530*x^4 + 7489*x^5 + 113289*x^6 +...
%e Related expansions.
%e A(x)^2 = 1 + 2*x + 9*x^2 + 92*x^3 + 1160*x^4 + 16374*x^5 +...
%e A(x)^5 = 1 + 5*x + 30*x^2 + 300*x^3 + 3775*x^4 + 53226*x^5 +...
%e A(x)^6 = 1 + 6*x + 39*x^2 + 392*x^3 + 4935*x^4 + 69600*x^5 +...
%e where 1+x = A(x)^2 + A(x)^5 - A(x)^6.
%o (PARI) /* From 1+x = A(x)^2 + A(x)^5 - A(x)^6: */
%o {a(n)=local(A=[1, 1]); for(i=1, n, A=concat(A, 0); A[#A]=-Vec(Ser(A)^2+Ser(A)^5-Ser(A)^6)[#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 - 10*x^3 - 10*x^4 - 5*x^5 - x^6 + x^2*O(x^n)));polcoeff(A,n)}
%o for(n=0, 25, print1(a(n) , ", "))
%Y Cf. A249926, A249927, A249929, A249930, A249931, A249932.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Nov 27 2014
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