A181999 G.f. satisfies: A(x) = A(x^2) + x*A(x)^2.

1, 1, 3, 7, 23, 69, 233, 791, 2807, 10089, 37043, 137659, 518009, 1967409, 7536249, 29072599, 112863479, 440560817, 1728178583, 6808762011, 26931287867, 106903064137, 425723073033, 1700377605835, 6809856020309, 27340764872261, 110022229116359, 443683568475459

Offset

0,3

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..300

Formula

G.f. satisfies: A(x) = (1 - sqrt(1 - 4*x*A(x^2))) / (2*x).

a(n) ~ c * d^n / n^(3/2), where d = 4.26223122317069895..., c = 0.643574350110058603... . - Vaclav Kotesovec, Aug 08 2014

Example

G.f.: A(x) = 1 + x + 3*x^2 + 7*x^3 + 23*x^4 + 69*x^5 + 233*x^6 + 791*x^7 +...
Related expansion:
A(x)^2 = 1 + 2*x + 7*x^2 + 20*x^3 + 69*x^4 + 226*x^5 + 791*x^6 +...

Prog

(PARI) {a(n)=local(A=1+x); for(i=1, n, A=subst(A, x, x^2+x*O(x^n))+x*A^2); polcoeff(A, n)}
for(n=0, 30, print1(a(n), ", "))

Crossrefs

Sequence in context: A148697 A148698 A148699 * A148700 A151268 A148701

Adjacent sequences: A181996 A181997 A181998 * A182000 A182001 A182002

Keyword

nonn

Author

Paul D. Hanna, Apr 05 2012

Status

approved