A214764 G.f. satisfies: A(x) = 1/A(-x*A(x)^4).

1, 2, 10, 60, 390, 2660, 18772, 138984, 1107686, 9576100, 87944188, 830857464, 7876505340, 73967614584, 685644645896, 6289047266480, 57465415636166, 528315307772004, 4947263762389484, 47785581838822232, 480797992896880788, 5058812497153271912

Offset

0,2

Comments

Compare to: W(x) = 1/W(-x*W(x)^4) when W(x) = Sum_{n>=0} (2*n+1)^(n-1)*x^n/n!.

Compare to: B(x) = 1/B(-x*B(x)^4) when B(x) = 1/(1-8*x)^(1/4) = g.f. of A004981.

An infinite number of functions G(x) satisfy (*) G(x) = 1/G(-x*G(x)^4); for example, (*) is satisfied by G(x) = W(m*x), where W(x) = Sum_{n>=0} (2*n+1)^(n-1)*x^n/n!.

Links

Table of n, a(n) for n=0..21.

Formula

The g.f. of this sequence is the limit of the recurrence:

(*) G_{n+1}(x) = (G_n(x) + 1/G_n(-x*G_n(x)^4))/2 starting at G_0(x) = 1+2*x.

Example

G.f.: A(x) = 1 + 2*x + 10*x^2 + 60*x^3 + 390*x^4 + 2660*x^5 + 18772*x^6 +...
A(x)^4 = 1 + 8*x + 64*x^2 + 512*x^3 + 4096*x^4 + 32800*x^5 + 263168*x^6 +...

Prog

(PARI) {a(n)=local(A=1+2*x); for(i=0, n, A=(A+1/subst(A, x, -x*A^4+x*O(x^n)))/2); polcoeff(A, n)}
for(n=0, 31, print1(a(n), ", "))

Crossrefs

Cf. A214761, A214762, A214763, A214765, A214766, A214767, A214768, A214769.

Sequence in context: A341924 A350665 A004981 * A365554 A137571 A215002

Adjacent sequences: A214761 A214762 A214763 * A214765 A214766 A214767

Keyword

nonn

Author

Paul D. Hanna, Jul 29 2012

Status

approved