A168602 G.f. satisfies: A(x) = 1 + x*A(x)^2*A(2x).

1, 1, 4, 29, 348, 7078, 257400, 17567085, 2321150956, 603642816242, 311497277686152, 320223587003352866, 657101019781977963480, 2694116441965648648689708, 22080982977564915182409980400

Offset

0,3

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..80

Formula

a(0) = 1; a(n) = Sum_{i=0..n-1} Sum_{j=0..n-i-1} 2^i * a(i) * a(j) * a(n-i-j-1). - Ilya Gutkovskiy, Nov 12 2021

a(n) ~ c * 2^(n*(n-1)/2), where c = 8.922794036651587033803872123786584213844... - Vaclav Kotesovec, Nov 13 2021

Example

G.f.: A(x) = 1 + x + 4*x^2 + 29*x^3 + 348*x^4 + 7078*x^5 +...
A(x)^2 = 1 + 2*x + 9*x^2 + 66*x^3 + 770*x^4 + 15084*x^5 +...

Mathematica

nmax = 20; A[_] = 0; Do[A[x_] = 1 + x*A[x]^2*A[2*x] + 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) ); polcoeff(A, n)}

Crossrefs

Cf. A168603.

Sequence in context: A256006 A137646 A231498 * A368452 A000798 A135485

Adjacent sequences: A168599 A168600 A168601 * A168603 A168604 A168605

Keyword

nonn

Author

Paul D. Hanna, Dec 05 2009

Status

approved