A182488 G.f. satisfies: A(x) = 1 + x*A(x) * A( x^2*A(x)^2 ).

1, 1, 1, 2, 5, 12, 30, 80, 221, 624, 1798, 5271, 15662, 47052, 142686, 436187, 1342669, 4158048, 12945758, 40497415, 127225426, 401222453, 1269712425, 4030877287, 12833659158, 40968993548, 131106215470, 420507819784, 1351562339222, 4352564765053, 14042486582525

Offset

0,4

Links

Table of n, a(n) for n=0..30.

Formula

G.f. satisfies: A( x/(1 + x*A(x^2)) ) = 1 + x*A(x^2).

Example

G.f.: A(x) = 1 + x + x^2 + 2*x^3 + 5*x^4 + 12*x^5 + 30*x^6 + 80*x^7 +...
Related expansions.
1/(1+x*A(x^2)) = 1 - x + x^2 - 2*x^3 + 3*x^4 - 5*x^5 + 8*x^6 - 14*x^7 +...
compare to the series reversion of x*A(x), which begins:
x - x^2 + x^3 - 2*x^4 + 3*x^5 - 5*x^6 + 8*x^7 - 14*x^8 + 23*x^9 +...

Prog

(PARI) {a(n)=local(A=1+x); for(i=1, n, A=1/x*serreverse(x/(1+x*subst(A, x, x^2 +x*O(x^n))))); polcoeff(A, n)}
for(n=0, 31, print1(a(n), ", "))

Crossrefs

Sequence in context: A003089 A213263 A179544 * A363912 A261788 A112412

Adjacent sequences: A182485 A182486 A182487 * A182489 A182490 A182491

Keyword

nonn

Author

Paul D. Hanna, May 02 2012

Status

approved