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

Author

Paul D. Hanna, Jun 06 2012

Keywords

• nonn

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).

Examples

			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 +...
		

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.

Programs

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), ", "))