A184508 G.f. satisfies: A(x) = B(x*A(x)), where B(x) is the g.f. of A184506.

1, 1, 1, 3, 6, 33, 79, 661, 1564, 19357, 39568, 751741, 1134328, 36687892, 30140408, 2174316050, 65676634, 152761870350, -126456152854, 12495122715428, -21554431449186, 1173014849466128, -3099148178903788, 124924998253897302, -445406039525657880

Offset

0,4

Comments

G.f. B(x) of A184506 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 A184507 and A(x) 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 + 3*x^3 + 6*x^4 + 33*x^5 + 79*x^6 + 661*x^7 +...
Related expansions.
A(x) = B(x*A(x)) where B(x) = A(x/B(x)) is the g.f. of A184506:
B(x) = 1 + x + 2*x^3 - 3*x^4 + 27*x^5 - 91*x^6 + 723*x^7 -+...
Also, A(x) = F(x*A(x)^2) where F(x) = A(x/F(x)^2) is the g.f. of A184507:
F(x) = 1 + x - x^2 + 4*x^3 - 16*x^4 + 86*x^5 - 482*x^6 + 3074*x^7 +...

Prog

 (PARI) {a(n)=local(A=1, F=1+x+x*O(x^n)); for(i=1, n, A=1/x*serreverse(x/F); F=1+A*serreverse(x*F) + x*O(x^n)); polcoeff(A, n)}
for(n=0, 30, print1(a(n), ", "))

Crossrefs

Cf. A184506, A184507.

Sequence in context: A284633 A192166 A297444 * A101142 A298679 A261885

Adjacent sequences: A184505 A184506 A184507 * A184509 A184510 A184511

Keyword

sign

Author

Paul D. Hanna, Dec 22 2012

Status

approved