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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.
2
1, 1, 3, 13, 69, 420, 2845, 21187, 173554, 1584768, 16617329, 210472915, 3451735696, 78546037008, 2582920450824, 123477535651607, 8494578276132389, 832041256283517038, 115176854055075767837, 22420312200544123743720
OFFSET
0,3
LINKS
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
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jul 08 2011
STATUS
approved