A213103 G.f. satisfies: A(x) = 1 + x/A(-x*A(x)^12)^4.

1, 1, 4, 42, 420, 5779, 83104, 1306684, 21283504, 356648125, 6100611232, 105634585546, 1845124077000, 32368064972555, 568794055227200, 9991239094888864, 175142529040285920, 3060545399532144497, 53279047286232892928, 923884653765128839312, 15965368274611453269820

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(76). - 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 + 42*x^3 + 420*x^4 + 5779*x^5 + 83104*x^6 +...
Related expansions:
A(x)^12 = 1 + 12*x + 114*x^2 + 1252*x^3 + 14775*x^4 + 193956*x^5 +...
A(-x*A(x)^12)^4 = 1 - 4*x - 26*x^2 - 148*x^3 - 2415*x^4 - 33192*x^5 -...

Mathematica

m = 21; A[_] = 1; Do[A[x_] = 1 + x/A[-x A[x]^12]^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^12, 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, A213101, A213102, A213104, A213105.

Sequence in context: A219980 A321957 A037296 * A085954 A046719 A366819

Adjacent sequences: A213100 A213101 A213102 * A213104 A213105 A213106

Keyword

sign

Author

Paul D. Hanna, Jun 05 2012

Status

approved