A178852 G.f. satisfies: A(x) = x/(x - B(x^2)) where B(x/A(x)) = x and B(x) is the g.f. of A141200.

1, 1, 1, 2, 3, 6, 10, 21, 37, 79, 144, 311, 580, 1262, 2393, 5236, 10055, 22095, 42857, 94495, 184784, 408557, 804331, 1782470, 3529190, 7836235, 15591086, 34676360, 69284645, 154320310, 309480750, 690193910, 1388679639, 3100467566

Offset: 0

Author

Paul D. Hanna, Aug 11 2010

Keywords

• nonn

Comments

The g.f. of A141200 satisfies: B(x) = x + B(B(x)^2).

Examples

			G.f.: A(x) = 1 + x + x^2 + 2*x^3 + 3*x^4 + 6*x^5 + 10*x^6 + 21*x^7 +...
If B(x) = g.f. of A141200, with B(x/A(x)) = x and B(x) = x + B(B(x)^2), then
B(x) = x + x^2 + 2*x^3 + 6*x^4 + 20*x^5 + 72*x^6 + 272*x^7 +... where
x/A(x) = x - (x^2 + x^4 + 2*x^6 + 6*x^8 + 20*x^10 + 72*x^12 + 272*x^14 +...)
A(B(x)) = B(x)/x = 1 + x + 2*x^2 + 6*x^3 + 20*x^4 + 72*x^5 + 272*x^6 +...
		

Links

• Paul D. Hanna, Table of n, a(n) for n = 0..512

Crossrefs

Cf. A141200.

Programs

PARI

{a(n)=local(A=1+x+x^2*O(x^n)); for(i=0,#binary(n)+1, A=x/(x-subst(serreverse(x/A), x, x^2+x^2*O(x^n)))) ; polcoeff(A, n)}
for(n=0,40,print1(a(n),", "))

Formula

a(n) ~ c * d^n / n^(3/2), where d = 2.20085985704067535258..., c = 4.25914484723... if n is even and c = 4.40480643955... if n is odd. - Vaclav Kotesovec, Dec 02 2014