A171184 G.f. satisfies: A(x) = A(x)^2 - x*A(2x).

1, 1, 1, 2, 11, 150, 4474, 277044, 34897875, 8863484966, 4520306307806, 4619735172579132, 9451969086159465470, 38696352180977336223228, 316923105439684775855164884, 5191834235882300670847354499880

Offset

0,4

Links

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

Formula

a(n) = 2^(n-1)*a(n-1) - Sum_{k=1..n-1} a(k)*a(n-k) for n>0 with a(0)=1.

G.f.: A(x) = 1 + x*A(2x)/A(x).

a(n) ~ c * 2^(n*(n-1)/2), where c = 0.1279729718630988916686793555289366866035815816364398379... . - Vaclav Kotesovec, Aug 08 2014

Example

G.f.: A(x) = 1 + x + x^2 + 2*x^3 + 11*x^4 + 150*x^5 + 4474*x^6 +...
A(x)^2 = 1 + 2*x + 3*x^2 + 6*x^3 + 27*x^4 + 326*x^5 + 9274*x^6 +...

Prog

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

Crossrefs

Sequence in context: A185245 A006122 A111014 * A297676 A049462 A227328

Adjacent sequences: A171181 A171182 A171183 * A171185 A171186 A171187

Keyword

nonn

Author

Paul D. Hanna, Dec 09 2009

Status

approved