A210839 G.f. satisfies: A(x) = x + A( x*A(x)/(1 - x*A(x)) ).

1, 1, 1, 3, 7, 17, 45, 121, 333, 937, 2675, 7735, 22613, 66711, 198361, 593873, 1788697, 5416097, 16477471, 50342595, 154397465, 475169249, 1466983101, 4542061223, 14100318843, 43879550851, 136858661589, 427747723605, 1339505345521, 4202281084715, 13205593222009

Offset

1,4

Comments

Compare the g.f. to the trivial identity:

G(x) = x + G( x*G(x)/(1 + x*G(x)) ) which holds when G(x) = x/(1-x).

Links

Table of n, a(n) for n=1..31.

Formula

G.f. satisfies: A(-A(-x)) = x.

Example

G.f.: A(x) = x + x^2 + x^3 + 3*x^4 + 7*x^5 + 17*x^6 + 45*x^7 + 121*x^8 +...
Related expansion:
x*A(x)/(1-x*A(x)) = x^2 + x^3 + 2*x^4 + 5*x^5 + 11*x^6 + 28*x^7 + 73*x^8 + 195*x^9 + 536*x^10 + 1501*x^11 + 4269*x^12 + 12306*x^13 + 35869*x^14 +...

Prog

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

Crossrefs

Sequence in context: A018025 A018026 A087953 * A261235 A211281 A233656

Adjacent sequences: A210836 A210837 A210838 * A210840 A210841 A210842

Keyword

nonn

Author

Paul D. Hanna, May 10 2012

Status

approved