A184507 G.f. satisfies: A(x) = B(x/A(x)), where B(x) is the g.f. of A184506.

1, 1, -1, 4, -16, 86, -482, 3074, -20478, 147227, -1101843, 8702605, -71285202, 609348589, -5385150192, 49346937185, -466332024088, 4550830295128, -45705121373663, 472675376094619, -5022099348895724, 54826872973024796, -613998703071634703, 7052884860025205276

Offset

0,4

Comments

The g.f. B(x) of A184506 satisfies B(x) = 1 + x*G(x)/A(x) where G(x) = B(x*G(x)) = A(x*G(x)^2) is the g.f. of A184508 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..23.

Example

 G.f.: A(x) = 1 + x - x^2 + 4*x^3 - 16*x^4 + 86*x^5 - 482*x^6 + 3074*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) = G(x/A(x)^2) where  G(x) = A(x*G(x)^2) is the g.f. of A184508:
G(x) = 1 + x + x^2 + 3*x^3 + 6*x^4 + 33*x^5 + 79*x^6 + 661*x^7 +...

Prog

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

Crossrefs

Cf. A184506, A184508.

Sequence in context: A006681 A074876 A238722 * A165964 A300279 A321238

Adjacent sequences: A184504 A184505 A184506 * A184508 A184509 A184510

Keyword

sign

Author

Paul D. Hanna, Dec 22 2012

Status

approved