A184510 G.f. satisfies: A(x) = B(x/A(x)), where B(x) is the g.f. of A184509.

1, 1, 1, 1, 4, 22, 103, 565, 3650, 24574, 174621, 1326012, 10552612, 87581914, 758382533, 6820324763, 63533751777, 612270354128, 6092311420096, 62498687197246, 660267713966489, 7174908370818956, 80115656652409638, 918403116546918196, 10799109424669566696

Offset

0,5

Comments

The g.f. B(x) of A184509 satisfies B(x) = 1 + x*A(x)*G(x) where G(x) = B(x*G(x)) = A(x*G(x)^2) is the g.f. of A184511 and A(x) = B(x/A(x)) = G(x/A(x)^2) is the g.f. of this sequence.

Links

Table of n, a(n) for n=0..24.

Example

G.f.: A(x) = 1 + x + x^2 + x^3 + 4*x^4 + 22*x^5 + 103*x^6 + 565*x^7 +...
G.f.: A(x) = B(x/A(x)) where B(x) = A(x*B(x)) is the g.f. of A184509:
B(x) = 1 + x + 2*x^2 + 5*x^3 + 17*x^4 + 78*x^5 + 423*x^6 + 2547*x^7 +...
G.f.: A(x) = G(x/A(x)^2) where  G(x) = A(x*G(x)^2) is the g.f. of A184511:
G(x) = 1 + x + 3*x^2 + 12*x^3 + 58*x^4 + 324*x^5 + 2016*x^6 + 13629*x^7 +...

Prog

(PARI) {a(n)=local(A=1+x+x*O(x^n)); for(i=1, n, B=1/x*serreverse(x/A); A=x/serreverse(x*(1+A*serreverse(x/B)+x*O(x^n)))); polcoeff(A, n)}

Crossrefs

Cf. A184509, A184511.

Sequence in context: A017970 A220740 A099013 * A184701 A001436 A224243

Adjacent sequences: A184507 A184508 A184509 * A184511 A184512 A184513

Keyword

nonn

Author

Paul D. Hanna, Dec 30 2011

Status

approved