A143597 G.f. satisfies: A(x) = 1 + x*A(2x)*A(-x).

1, 1, 1, 3, 19, 297, 8953, 572155, 72116459, 18460128753, 9414877745601, 9640779710687955, 19725063387945457219, 80793830752052788593529, 661701532957780822275151305, 10841317673677535233876159099755

Offset

0,4

Links

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

Formula

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

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

Example

G.f.: A(x) = 1 + x + x^2 + 3*x^3 + 19*x^4 + 297*x^5 + 8953*x^6 +...
A(x) = 1 + x*A(2x)*[1 - x*A(-2x)*[1 + x*A(2x)*[1 - x*A(-2x)*[1 +...]]]].

Prog

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

Crossrefs

Sequence in context: A231620 A268646 A356512 * A224681 A115705 A136171

Adjacent sequences: A143594 A143595 A143596 * A143598 A143599 A143600

Keyword

nonn

Author

Paul D. Hanna, Aug 28 2008

Status

approved