A120953 G.f. A(x) equals series_reversion(x/F(x))/x where F(x) is the g.f. of A120952; a(2*n+1) = 0 for n>=1.

1, 1, 3, 0, -65, 0, 4998, 0, -691749, 0, 142819050, 0, -40447525482, 0, 14988562779660, 0, -7042958511356013, 0, 4098696561237950274, 0, -2898331335691958097918, 0, 2450632554538246780555476, 0, -2443617360583149618790999650, 0

Offset

0,3

Links

Table of n, a(n) for n=0..25.

Formula

G.f. satisfies: A(x) = F(x*A(x)) and F(x) = A(x/F(x)) where F(x) = g.f. of A120952.

Example

A(x) = 1 + x + 3*x^2 - 65*x^4 + 4998*x^6 - 691749*x^8 +-...
The g.f. of A120952 is:
F(x) = 1 + x + 2*x^2 - 7*x^3 - 58*x^4 + 369*x^5 + 4572*x^6 --++...

Prog

(PARI) {a(n)=local(A=[1, 1]); for(i=1, n, if(#A%2==1, A=concat(A, t); A[ #A]=-subst(Vec(serreverse(x/Ser(A)))[ #A], t, 0)); if(#A%2==0, A=concat(A, t); A[ #A]=subst(Vec(serreverse(x*Ser(A)))[ #A], t, 0))); Vec(serreverse(x/Ser(A)))[n+1]}

Crossrefs

Cf. A120952, A120954.

Sequence in context: A264882 A012759 A296621 * A009784 A276909 A276910

Adjacent sequences: A120950 A120951 A120952 * A120954 A120955 A120956

Keyword

sign

Author

Paul D. Hanna, Jul 19 2006

Status

approved