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G.f. A(x) satisfies: A(x) = A(x^3)^(1/3) + 3*x.
1

%I #3 Mar 30 2012 18:36:46

%S 1,3,0,1,0,0,-1,0,0,2,0,0,-4,0,0,9,0,0,-22,0,0,55,0,0,-142,0,0,376,0,

%T 0,-1011,0,0,2758,0,0,-7614,0,0,21220,0,0,-59630,0,0,168759,0,0,

%U -480533,0,0,1375676,0,0,-3957075,0,0,11430582,0,0,-33144264,0,0,96434321,0,0,-281447954,0,0,823734157,0,0,-2417092933,0,0

%N G.f. A(x) satisfies: A(x) = A(x^3)^(1/3) + 3*x.

%C Self-convolution cube of A107092.

%e A(x) = 1 + 3*x + x^3 - x^6 + 2*x^9 - 4*x^12 + 9*x^15 - 22*x^18 +...

%e A(x^3)^(1/3) = 1 + x^3 - x^6 + 2*x^9 - 4*x^12 + 9*x^15 - 22*x^18 +...

%o (PARI) {a(n)=local(A=1+x);for(i=1,n,A=(subst(A,x,x^3)+3*x+x*O(x^n))^(1/3)); polcoeff(A^3,n,x)}

%Y Cf. A107092.

%K sign

%O 0,2

%A _Paul D. Hanna_, May 11 2005