|
%I #3 Jun 06 2012 19:53:29
%S 1,1,4,25,176,1431,12526,117850,1167446,12080563,129326575,1422908670,
%T 15999766613,183070661566,2124252427416,24929036429880,
%U 295250330398281,3523043486823439,42294807342916249,510274778010082846,6181011777164665559,75112032752942278141
%N G.f. satisfies: A(x) = 1/(1 - x/A(-x*A(x)^8)^3).
%C Compare g.f. to:
%C (1) G(x) = 1/(1 - x/G(-x*G(x)^3)^1) when G(x) = 1/(1 - x*G(x)^1) (A000108).
%C (2) G(x) = 1/(1 - x/G(-x*G(x)^5)^2) when G(x) = 1/(1 - x*G(x)^2) (A001764).
%C (3) G(x) = 1/(1 - x/G(-x*G(x)^7)^3) when G(x) = 1/(1 - x*G(x)^3) (A002293).
%C (4) G(x) = 1/(1 - x/G(-x*G(x)^9)^4) when G(x) = 1/(1 - x*G(x)^4) (A002294).
%e G.f.: A(x) = 1 + x + 4*x^2 + 25*x^3 + 176*x^4 + 1431*x^5 + 12526*x^6 +...
%e Related expansions:
%e A(x)^8 = 1 + 8*x + 60*x^2 + 480*x^3 + 3998*x^4 + 34968*x^5 + 318888*x^6 +...
%e 1/A(-x*A(x)^8)^3 = 1 + 3*x + 18*x^2 + 121*x^3 + 987*x^4 + 8646*x^5 + 82244*x^6 +...
%o (PARI) {a(n)=local(A=1+x+x*O(x^n)); for(i=1, n, A=1/(1-x/subst(A^3, x, -x*subst(A^8, x, x+x*O(x^n)))) ); polcoeff(A, n)}
%o for(n=0, 30, print1(a(n), ", "))
%Y Cf. A213225, A213226, A213227, A213228, A213229, A213230, A213232, A213233.
%Y Cf. A213091, A213092, A213093, A213094, A213095, A213096, A213098.
%Y Cf. A213099, A213100, A213101, A213102, A213103, A213104, A213105.
%Y Cf. A213108, A213109, A213110, A213111, A213112, A213113.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Jun 06 2012
|
