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URL: https://oeis.org/A213102

⇱ A213102 - OEIS

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A213102
G.f. satisfies: A(x) = 1 + x/A(-x*A(x)^9)^4.
18
1, 1, 4, 30, 240, 2433, 26388, 315726, 3958452, 51863952, 698988716, 9637772716, 135161761860, 1920878419569, 27583547221596, 399310273694328, 5817100622299116, 85152975761167179, 1251046169511714720, 18428780031111768466, 271964652432415737596
OFFSET
0,3
COMMENTS
Compare definition of g.f. to:
(1) B(x) = 1 + x/B(-x*B(x)) when B(x) = 1/(1-x).
(2) C(x) = 1 + x/C(-x*C(x)^3)^2 when C(x) = 1 + x*C(x)^2 (A000108).
(3) D(x) = 1 + x/D(-x*D(x)^5)^3 when D(x) = 1 + x*D(x)^3 (A001764).
(4) E(x) = 1 + x/E(-x*E(x)^7)^4 when E(x) = 1 + x*E(x)^4 (A002293).
(5) F(x) = 1 + x/F(-x*F(x)^9)^5 when F(x) = 1 + x*F(x)^5 (A002294).
The first negative term is a(142). - Georg Fischer, Feb 16 2019
LINKS
EXAMPLE
G.f.: A(x) = 1 + x + 4*x^2 + 30*x^3 + 240*x^4 + 2433*x^5 + 26388*x^6 +...
Related expansions:
A(x)^9 = 1 + 9*x + 72*x^2 + 642*x^3 + 6030*x^4 + 61551*x^5 + 670344*x^6 +...
A(-x*A(x)^9)^4 = 1 - 4*x - 14*x^2 - 64*x^3 - 797*x^4 - 8188*x^5 - 104090*x^6 -...
MATHEMATICA
m = 21; A[_] = 1; Do[A[x_] = 1 + x/A[-x A[x]^9]^4 + O[x]^m, {m}];
CoefficientList[A[x], x] (* Jean-François Alcover, Nov 06 2019 *)
PROG
(PARI) {a(n)=local(A=1+x+x*O(x^n)); for(i=1, n, A=1+x/subst(A^4, x, -x*subst(A^9, x, x+x*O(x^n))) ); polcoeff(A, n)}
for(n=0, 30, print1(a(n), ", "))
KEYWORD
sign
AUTHOR
Paul D. Hanna, Jun 05 2012
STATUS
approved