1,3

Limit_{n->inf} a(n)/2^((n-1)(n-2)/2) = Product{k=1..inf} 1/(1-1/2^k) = 3.462746619455... (cf. A065446). - Paul D. Hanna (pauldhanna(AT)juno.com), Jan 24 2005

It appears that the Hankel transform is 2^A002412(n). [From Paul Barry (pbarry(AT)wit.ie), Aug 01 2008]

a(n) = sum_{i=1}^{n-1} q^{(i-1)} a(i) a(n-i).

G.f. satisfies: A(x) = 2*x/(2-A(2*x)) = x/(1-x/(1-2*x/(1-2^2*x/(1-2^3*x/(1-...))))) (continued fraction). - Paul D. Hanna (pauldhanna(AT)juno.com), Jan 24 2005

(PARI) a(n)=if(n==1, 1, sum(i=1, n-1, 2^(i-1)*a(i)*a(n-i))) (Hanna)

(PARI) {a(n)=local(A); if(n<1, 0, A=vector(n); for(k=1, n, A[k]=if(k<2, 1, sum(i=1, k-1, 2^i*A[i]*A[k-i])/2)); A[n])} /* Michael Somos Jan 30 2005 */

(PARI) {a(n)=local(A); if(n<1, 0, A=O(x); for(k=1, n, A=x/(1-subst(A, x, 2*x)/2)); polcoeff(A, n))} /* Michael Somos Jan 30 2005 */

Cf. A065446.

Sequence in context: A163884 A052143 A069856 this_sequence A053934 A159592 A126443

Adjacent sequences: A015080 A015081 A015082 this_sequence A015084 A015085 A015086

nonn

Olivier Gerard (olivier.gerard(AT)gmail.com)