A213229 G.f. satisfies: A(x) = 1/(1 - x/A(-x*A(x)^7)^2).

1, 1, 3, 16, 93, 649, 4924, 40221, 344817, 3058115, 27798895, 257009431, 2404734586, 22679499148, 214947515333, 2042353663088, 19417906390395, 184458621283607, 1748712359825873, 16530801697256737, 155736745914813741, 1461877902947680987, 13674142992787617967

Offset

0,3

Comments

Compare g.f. to:

(1) G(x) = 1/(1 - x/G(-x*G(x)^3)^1) when G(x) = 1/(1 - x*G(x)^1) (A000108).

(2) G(x) = 1/(1 - x/G(-x*G(x)^5)^2) when G(x) = 1/(1 - x*G(x)^2) (A001764).

(3) G(x) = 1/(1 - x/G(-x*G(x)^7)^3) when G(x) = 1/(1 - x*G(x)^3) (A002293).

(4) G(x) = 1/(1 - x/G(-x*G(x)^9)^4) when G(x) = 1/(1 - x*G(x)^4) (A002294).

Links

Table of n, a(n) for n=0..22.

Example

 G.f.: A(x) = 1 + x + 3*x^2 + 16*x^3 + 93*x^4 + 649*x^5 + 4924*x^6 +...
Related expansions:
A(x)^7 = 1 + 7*x + 42*x^2 + 273*x^3 + 1862*x^4 + 13531*x^5 + 104062*x^6 +...
1/A(-x*A(x)^7)^2 = 1 + 2*x + 11*x^2 + 60*x^3 + 431*x^4 + 3302*x^5 + 27421*x^6 +..

Prog

 (PARI) {a(n)=local(A=1+x+x*O(x^n)); for(i=1, n, A=1/(1-x/subst(A^2, x, -x*subst(A^7, x, x+x*O(x^n)))) ); polcoeff(A, n)}
for(n=0, 30, print1(a(n), ", "))

Crossrefs

Cf. A213225, A213226, A213227, A213228, A213230, A213231, A213232, A213233.

Cf. A213091, A213092, A213093, A213094, A213095, A213096, A213098.

Cf. A213099, A213100, A213101, A213102, A213103, A213104, A213105.

Cf. A213108, A213109, A213110, A213111, A213112, A213113.

Sequence in context: A305852 A221764 A371742 * A323968 A074555 A137644

Adjacent sequences: A213226 A213227 A213228 * A213230 A213231 A213232

Keyword

nonn

Author

Paul D. Hanna, Jun 06 2012

Status

approved