A184511 G.f. satisfies: A(x) = B(x*A(x)), where B(x) is the g.f. of A184509.

1, 1, 3, 12, 58, 324, 2016, 13629, 98644, 756852, 6110309, 51620412, 454430088, 4155005770, 39354004740, 385288338532, 3892135131803, 40507984800374, 433792913778315, 4774455016668509, 53954983308058733, 625485598856053837, 7432389116043114682

Offset

0,3

Links

Table of n, a(n) for n=0..22.

Formula

G.f. B(x) of A184509 satisfies: B(x) = 1 + x*A(x)*F(x) where F(x) = B(x/F(x)) = A(x/F(x)^2) is the g.f. of A184510 and A(x) is the g.f. of this sequence.

Example

G.f.: A(x) = 1 + x + 3*x^2 + 12*x^3 + 58*x^4 + 324*x^5 + 2016*x^6 +...
where A(x) = B(x*A(x)) and 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 +...
Also, A(x) = F(x*A(x)^2) where F(x) = A(x/F(x)^2) is the g.f. of A184510:
F(x) = 1 + x + x^2 + x^3 + 4*x^4 + 22*x^5 + 103*x^6 + 565*x^7 +...
The product A(x)*F(x) begins:
A(x)*F(x) = 1 + 2*x + 5*x^2 + 17*x^3 + 78*x^4 + 423*x^5 + 2547*x^6 +...
where B(x) = 1 + x*A(x)*F(x).

Prog

(PARI) {a(n)=local(A=1+x+x*O(x^n), F); for(i=1, n, F=(x/serreverse(x*A^2+x*O(x^n)))^(1/2); A=1/x*serreverse(x/(1+x*A*F)) ); polcoeff(A, n)}

Crossrefs

Cf. A184509, A184510.

Sequence in context: A115086 A258173 A196708 * A125276 A001426 A059440

Adjacent sequences: A184508 A184509 A184510 * A184512 A184513 A184514

Keyword

nonn

Author

Paul D. Hanna, Sep 13 2011

Status

approved