A172394 - OEIS

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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

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,7

COMMENTS

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

LINKS

Table of n, a(n) for n=0..33.

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.

EXAMPLE

G.f.: A(x) = 1 - x - x^2 + x^4 - 4*x^6 + 27*x^8 - 248*x^10 +...