A168603 G.f. satisfies: A(x) = 1 + x*A(x)^2*A(2x)^2.

1, 1, 6, 73, 1578, 60582, 4276284, 574950725, 150783454338, 78124426877002, 80472666325118724, 165293072210433580170, 678034405564452384600036, 5558530569192415381768200652, 91104334435045362173635840712184, 2985853607256120630265759379554756269

Offset

0,3

Links

Table of n, a(n) for n=0..15.

Formula

a(n) ~ c * 2^(n*(n+1)/2), where c = 2.246717964359561210869708946140382812767... - Vaclav Kotesovec, Nov 13 2021

Example

G.f.: A(x) = 1 + x + 6*x^2 + 73*x^3 + 1578*x^4 + 60582*x^5 +...
A(x)^2 = 1 + 2*x + 13*x^2 + 158*x^3 + 3338*x^4 + 125196*x^5 +...

Mathematica

nmax = 20; A[_] = 0; Do[A[x_] = 1 + x*A[x]^2*A[2*x]^2 + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x] (* Vaclav Kotesovec, Nov 13 2021 *)

Prog

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

Crossrefs

Cf. A168602.

Sequence in context: A381430 A135594 A346960 * A244689 A058793 A066171

Adjacent sequences: A168600 A168601 A168602 * A168604 A168605 A168606

Keyword

nonn

Author

Paul D. Hanna, Dec 05 2009

Status

approved