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A143558 G.f. satisfies: A(x) = 1 + x*A(x)^5/A(-x)^5. 4

%I #6 Jun 04 2012 13:13:33

%S 1,1,10,50,570,4450,56202,501970,6676410,63799490,875391370,

%T 8715058802,122088479930,1249437863970,17764858122250,185445650940690,

%U 2666213981716282,28252030821781890,409717783914784010

%N G.f. satisfies: A(x) = 1 + x*A(x)^5/A(-x)^5.

%F G.f. satisfies: A(x) = 1 + x^2/(1 - A(-x)).

%F G.f. satisfies: A(x) = 1 + x^2 + x*A(x)^5/A(-x)^4.

%F G.f. satisfies: (A(x) - 1)^4 = ( 1 - (1+x^2)/A(x) )^5/x = x^4*A(x)^20/A(-x)^20.

%F G.f.: A(x) = (1+x^2)*G(x) where G(x) = 1 + x*G(x)^5/G(-x)^4.

%e G.f. A(x) = 1 + x + 10*x^2 + 50*x^3 + 570*x^4 + 4450*x^5 + 56202*x^6 +...

%e A(x)/A(-x) = 1 + 2*x + 2*x^2 + 82*x^3 + 162*x^4 + 7202*x^5 + 17442*x^6 +...

%e A(x)^4/A(-x)^4 = 1 + 8*x + 32*x^2 + 408*x^3 + 2752*x^4 + 38760*x^5 +...

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

%o (PARI) {a(n)=local(A=1+x*O(x^n));for(i=0,n,A=1+x*A^5/subst(A^5,x,-x));polcoeff(A,n)}

%Y Cf. A143555, A143556, A143557, A143559.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Aug 24 2008

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Last modified July 19 11:53 EDT 2024. Contains 374394 sequences. (Running on oeis4.)