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A184510
G.f. satisfies: A(x) = B(x/A(x)), where B(x) is the g.f. of A184509.
2
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.
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
Sequence in context: A017970 A220740 A099013 * A184701 A001436 A224243
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Dec 30 2011
STATUS
approved