A213101 G.f. satisfies: A(x) = 1 + x/A(-x*A(x)^8)^4.

1, 1, 4, 26, 188, 1627, 15172, 154904, 1670836, 18951217, 222682164, 2693625128, 33309537808, 419311915217, 5354144473084, 69169422070152, 902237854706616, 11863641066687085, 157052133090437332, 2090929291636792824, 27971914781646817864, 375725009230868446500

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(249). - Georg Fischer, Feb 16 2019

Links

Paul D. Hanna, Table of n, a(n) for n = 0..300

Example

G.f.: A(x) = 1 + x + 4*x^2 + 26*x^3 + 188*x^4 + 1627*x^5 + 15172*x^6 +...
Related expansions:
A(x)^8 = 1 + 8*x + 60*x^2 + 488*x^3 + 4150*x^4 + 37600*x^5 + 358788*x^6 +...
A(-x*A(x)^8)^4 = 1 - 4*x - 10*x^2 - 44*x^3 - 439*x^4 - 3884*x^5 - 42724*x^6 -...

Mathematica

m = 22; A[_] = 1; Do[A[x_] = 1 + x/A[-x A[x]^8]^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^8, x, x+x*O(x^n))) ); polcoeff(A, n)}
for(n=0, 30, print1(a(n), ", "))

Crossrefs

Cf. A000108, A001764, A002293, A002294, A213091, A213092, A213093, A213094, A213095, A213096, A213098, A213099, A213100, A213102, A213103, A213104, A213105.

Sequence in context: A107649 A371517 A052763 * A084211 A114496 A127086

Adjacent sequences: A213098 A213099 A213100 * A213102 A213103 A213104

Keyword

sign

Author

Paul D. Hanna, Jun 05 2012

Status

approved