A213226 G.f. satisfies: A(x) = 1/(1 - x/A(-x*A(x)^5)).

1, 1, 2, 7, 27, 122, 607, 3208, 17688, 99803, 571238, 3292738, 19001315, 109303307, 624615928, 3537913240, 19843769848, 110273489737, 608712132055, 3355449334452, 18624818099047, 105191779542849, 610586100129734, 3662333209225714, 22652502251884322

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..24.

Example

 G.f.: A(x) = 1 + x + 2*x^2 + 7*x^3 + 27*x^4 + 122*x^5 + 607*x^6 +...
Related expansions:
A(x)^5 = 1 + 5*x + 20*x^2 + 85*x^3 + 380*x^4 + 1801*x^5 + 9045*x^6 +...
1/A(-x*A(x)^5) = 1 + x + 4*x^2 + 14*x^3 + 66*x^4 + 336*x^5 + 1805*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^5, x, x+x*O(x^n)))) ); polcoeff(A, n)}
for(n=0, 30, print1(a(n), ", "))

Crossrefs

Cf. A213225, 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: A150645 A060017 A211475 * A058800 A357901 A342056

Adjacent sequences: A213223 A213224 A213225 * A213227 A213228 A213229

Keyword

nonn

Author

Paul D. Hanna, Jun 06 2012

Status

approved