A213333 G.f. satisfies: A(x) = x + A( A(x)^2/(1 - A(x) + A(x)^2) ).

1, 1, 3, 11, 45, 199, 925, 4457, 22059, 111473, 572759, 2983137, 15713985, 83570601, 448105431, 2419865513, 13149245161, 71844158103, 394456062591, 2175202340551, 12042184753415, 66904188191285, 372909667831073, 2084656444044577, 11685284016254365

Offset

1,3

Comments

Compare g.f. to: F(x) = x + F( -F(x)^2/(1 - F(x) + F(x)^2) ) when F(x) = x/(1+x).

Links

Table of n, a(n) for n=1..25.

Example

G.f.: A(x) = x + x^2 + 3*x^3 + 11*x^4 + 45*x^5 + 199*x^6 + 925*x^7 +...
Related expansions:
A(x)^2 = x^2 + 2*x^3 + 7*x^4 + 28*x^5 + 121*x^6 + 554*x^7 + 2639*x^8 +...
A(x)^2/(1 - A(x) + A(x)^2) = x^2 + 3*x^3 + 10*x^4 + 39*x^5 + 167*x^6 + 760*x^7 + 3607*x^8 + 88440*x^10 +...

Prog

(PARI) {a(n)=local(A=x+x^2); for(i=1, n, A=x+subst(A, x, A^2/(1-A+A^2+x*O(x^n)))); polcoeff(A, n)}
for(n=1, 30, print1(a(n), ", "))

Crossrefs

Cf. A213263, A213264.

Sequence in context: A187764 A372310 A151133 * A083886 A030866 A030941

Adjacent sequences: A213330 A213331 A213332 * A213334 A213335 A213336

Keyword

nonn

Author

Paul D. Hanna, Jun 08 2012

Status

approved