A192739 G.f. satisfies: A(x) = 1/(1 - x*A(x)/(1 - x*A(x)^2/(1 - x*A(x)^4/(1 - x*A(x)^8/(1 - ...))))), a recursive continued fraction.

1, 1, 3, 13, 69, 420, 2845, 21187, 173554, 1584768, 16617329, 210472915, 3451735696, 78546037008, 2582920450824, 123477535651607, 8494578276132389, 832041256283517038, 115176854055075767837, 22420312200544123743720

Offset

0,3

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..118

Example

G.f.: A(x) = 1 + x + 3*x^2 + 13*x^3 + 69*x^4 + 420*x^5 + 2845*x^6 +...
The g.f. A = A(x) satisfies:
A = 1 + x*A + x^2*(A^2 + A^3) + x^3*(A^3 + 2*A^4 + A^5 + A^7) + x^4*(A^4 + 3*A^5 + 3*A^6 + A^7 + 2*A^8 + 2*A^9 + A^11 + A^15) + x^5*(A^5 + 4*A^6 + 6*A^7 + 4*A^8 + 4*A^9 + 6*A^10 + 3*A^11 + 2*A^12 + 3*A^13 + A^15 + 2*A^16 + 2*A^17 + 2*A^19 + A^23 + A^31) +...
which is a series generated by the continued fraction expression.

Prog

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

Crossrefs

Cf. A192738.

Sequence in context: A352855 A088714 A067145 * A088368 A196794 A184818

Adjacent sequences: A192736 A192737 A192738 * A192740 A192741 A192742

Keyword

nonn

Author

Paul D. Hanna, Jul 08 2011

Status

approved