A139086 G.f. satisfies: A(x) = 3*x - x^2 - 2*Series_Reversion( A(x) ).

1, 1, 4, 30, 316, 4116, 62296, 1058418, 19764860, 400070484, 8693577528, 201394483524, 4947738765928, 128383644586440, 3507060528884560, 100587324451979478, 3022202483800235964, 94935204982349494092

Offset

1,3

Links

Table of n, a(n) for n=1..18.

Formula

a(n) = 2*(-1)^n*A139085(n) for n>2 with a(1)=a(2)=1.

Example

G.f.: A(x) = x + x^2 + 4*x^3 + 30*x^4 + 316*x^5 + 4116*x^6 +...
Series_Reversion(A(x)) = x - x^2 - 2*x^3 - 15*x^4 - 158*x^5 -...
which equals -G(-x) where G(x) = g.f. of A139085.

Prog

(PARI) {a(n)=local(A=x+x^2); if(n<1, 0, for(i=3, n+1, A=A+2*polcoeff(serreverse(A+x*O(x^i)), i)*x^i); polcoeff(A, n))}

Crossrefs

Cf. A139085.

Sequence in context: A145348 A052574 A158834 * A243244 A293022 A360766

Adjacent sequences: A139083 A139084 A139085 * A139087 A139088 A139089

Keyword

nonn

Author

Paul D. Hanna, Apr 08 2008

Status

approved