A172394 G.f. satisfies: A(x) = G(x/A(x)) where o.g.f. G(x) = A(x*G(x)) = Sum_{n>=0} A001464(n)*x^n.

1, -1, -1, 0, 1, 0, -4, 0, 27, 0, -248, 0, 2830, 0, -38232, 0, 593859, 0, -10401712, 0, 202601898, 0, -4342263000, 0, 101551822350, 0, -2573779506192, 0, 70282204726396, 0, -2057490936366320, 0, 64291032462761955, 0

Offset: 0

Author

Paul D. Hanna, Feb 06 2010

Keywords

• sign

Comments

The e.g.f. of A001464 is exp(-x-x^2/2) = Sum_{n>=0} A001464(n)*x^n/n!.

Examples

			G.f.: A(x) = 1 - x - x^2 + x^4 - 4*x^6 + 27*x^8 - 248*x^10 +...
where G(x) = A(x*G(x)) is the o.g.f. of A001464:
G(x) = 1 - x + 2*x^3 - 2*x^4 - 6*x^5 + 16*x^6 + 20*x^7 - 132*x^8 +...
while the e.g.f. of A001464 is given by:
exp(-x-x^2/2) = 1 - x + 2*x^3/3! - 2*x^4/4! - 6*x^5/5! + 16*x^6/6! +...
		

Crossrefs

Cf. A001464, A000699, A172395 (variant).

Programs

PARI

{a(n)=local(G=sum(m=0,n,m!*polcoeff(exp(-x-x^2/2+x*O(x^m)),m)*x^m)+x*O(x^n));polcoeff(x/serreverse(x*G),n)}

Formula

a(2n-2) = (-1)^(n-1)*A000699(n), where A000699(n) is the number of irreducible diagrams with 2n nodes, for n>=1.

a(2n-1) = 0 for n>=2, with a(1) = -1.