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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. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 19 03:18 EST 2020. Contains 331031 sequences. (Running on oeis4.)