A141201 G.f. satisfies: A(x)^(1/2) = x + A(x) + A(A(x)) + A(A(A(x))) + A(A(A(A(x)))) +...

1, 2, 5, 16, 56, 208, 804, 3202, 13046, 54120, 227812, 970596, 4177436, 18136008, 79326641, 349241700, 1546401412, 6882164584, 30767887372, 138114569908, 622270344740, 2812994557488, 12755010576700, 57996678526684

Offset

2,2

Links

Vaclav Kotesovec, Table of n, a(n) for n = 2..250

Formula

G.f.: A(x) = G(x)^2 where G(x) = g.f. of A141200.

a(n) ~ c / (n^(3/2) * r^n), where r = 0.2064501590536889244980412... (see A141200) and c = 0.051350746503831964896433888... . - Vaclav Kotesovec, Dec 02 2014

Example

G.f.: A(x) = x^2 + 2*x^3 + 5*x^4 + 16*x^5 + 56*x^6 + 208*x^7 +...
A(x)^(1/2) = x + x^2 + 2*x^3 + 6*x^4 + 20*x^5 + 72*x^6 + 272*x^7 +...
Related expansions:
A(A(x)) = x^4 + 4*x^5 + 16*x^6 + 64*x^7 + 260*x^8 + 1072*x^9 +...
A(A(A(x))) = x^8 + 8*x^9 + 48*x^10 + 256*x^11 + 1290*x^12 +...
A(A(A(A(x)))) = x^16 + 16*x^17 + 160*x^18 + 1280*x^19 + 8980*x^20 +...
where A(x)^(1/2) = x + A(x) + A(A(x)) + A(A(A(x))) + ...

Prog

(PARI) {a(n)=local(A=x+x^2); for(i=0, n, A=serreverse(x-subst(A, x, x^2+x^2*O(x^n)))); polcoeff(A^2, n)}

Crossrefs

Cf. A141200.

Sequence in context: A149974 A149975 A149976 * A149977 A147771 A052891

Adjacent sequences: A141198 A141199 A141200 * A141202 A141203 A141204

Keyword

nonn

Author

Paul D. Hanna, Jun 12 2008

Status

approved