A213105 G.f. satisfies: A(x) = 1 + x/A(-x*A(x)^12)^6.

1, 1, 6, 57, 614, 7716, 104322, 1529385, 23689968, 385885521, 6531397090, 114147452526, 2045979734964, 37435147640010, 696431496524796, 13134442980269397, 250527556214516892, 4824098879117797749, 93639919777995946446, 1830133457257882605430

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).

(6) G(x) = 1 + x/G(-x*G(x)^11)^6 when G(x) = 1 + x*G(x)^6 (A002295).

Links

Table of n, a(n) for n=0..19.

Example

G.f.: A(x) = 1 + x + 6*x^2 + 57*x^3 + 614*x^4 + 7716*x^5 + 104322*x^6 +...
Related expansions:
A(x)^12 = 1 + 12*x + 138*x^2 + 1696*x^3 + 21723*x^4 + 292836*x^5 +...
A(-x*A(x)^12)^6 = 1 - 6*x - 21*x^2 - 146*x^3 - 1959*x^4 - 25056*x^5 -...

Mathematica

m = 20; A[_] = 1; Do[A[x_] = 1 + x/A[-x A[x]^12]^6 + 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^6, x, -x*subst(A^12, x, x+x*O(x^n))) ); polcoeff(A, n)}
for(n=0, 30, print1(a(n), ", "))

Crossrefs

Cf. A213091, A213092, A213093, A213094, A213095, A213096.

Cf. A213098, A213099, A213100, A213101, A213102, A213103, A213104.

Sequence in context: A332620 A371521 A246235 * A138414 A349363 A130565

Adjacent sequences: A213102 A213103 A213104 * A213106 A213107 A213108

Keyword

nonn

Author

Paul D. Hanna, Jun 05 2012

Status

approved