A213226 - OEIS

%I #6 Aug 16 2024 18:48:16

%S 1,1,2,7,27,122,607,3208,17688,99803,571238,3292738,19001315,

%T 109303307,624615928,3537913240,19843769848,110273489737,608712132055,

%U 3355449334452,18624818099047,105191779542849,610586100129734,3662333209225714,22652502251884322

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

%C Compare g.f. to:

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

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

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

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

%e G.f.: A(x) = 1 + x + 2*x^2 + 7*x^3 + 27*x^4 + 122*x^5 + 607*x^6 +...

%e Related expansions:

%e A(x)^5 = 1 + 5*x + 20*x^2 + 85*x^3 + 380*x^4 + 1801*x^5 + 9045*x^6 +...

%e 1/A(-x*A(x)^5) = 1 + x + 4*x^2 + 14*x^3 + 66*x^4 + 336*x^5 + 1805*x^6 +...

%o (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)}

%o for(n=0, 30, print1(a(n), ", "))

%Y Cf. A213225, A213227, A213228, A213229, A213230, A213231, A213232, A213233.

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

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

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

%K nonn

%O 0,3

%A _Paul D. Hanna_, Jun 06 2012