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

0,4

Comments

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

Links

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

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

Example

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 +...

Prog

(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), ", "))

Crossrefs

Cf. A141200.

Sequence in context: A106741 A068991 A187491 * A215067 A008928 A124343

Adjacent sequences: A178849 A178850 A178851 * A178853 A178854 A178855

Keyword

nonn

Author

Paul D. Hanna, Aug 11 2010

Status

approved