A213225 G.f. satisfies: A(x) = 1/(1 - x/A(-x*A(x)^4)).

1, 1, 2, 6, 20, 76, 313, 1375, 6337, 30243, 148129, 739172, 3737993, 19077868, 97955307, 504707999, 2604312205, 13436676965, 69229324721, 355854322633, 1823672937884, 9314227843463, 47406130512872, 240498260267049, 1216833204738419, 6146116088495029

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..25.

Example

G.f.: A(x) = 1 + x + 2*x^2 + 6*x^3 + 20*x^4 + 76*x^5 + 313*x^6 +...
Related expansions:
A(x)^4 = 1 + 4*x + 14*x^2 + 52*x^3 + 201*x^4 + 816*x^5 + 3468*x^6 +...
1/A(-x*A(x)^4) = 1 + x + 3*x^2 + 9*x^3 + 35*x^4 + 146*x^5 + 656*x^6 +...

Prog

(PARI) {a(n)=local(A=1+x+x*O(x^n)); for(i=1, n, A=1/(1-x/subst(A, x, -x*subst(A^4, x, x+x*O(x^n)))) ); polcoeff(A, n)}
for(n=0, 30, print1(a(n), ", "))

Crossrefs

Cf. A213226, A213227, A213228, A213229, 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: A263904 A263898 A000898 * A195254 A150173 A150174

Adjacent sequences: A213222 A213223 A213224 * A213226 A213227 A213228

Keyword

nonn

Author

Paul D. Hanna, Jun 06 2012

Status

approved