A172395 G.f. satisfies: A(x) = G(x/A(x)) where o.g.f. G(x) = A(x*G(x)) = Sum_{n>=0} A000085(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, 2136017303903513184, 0

Offset

0,7

Comments

The e.g.f. of A000085 is exp(x+x^2/2) = Sum_{n>=0} A000085(n)*x^n/n!, where A000085(n) is the number of self-inverse permutations on n letters.

Links

Table of n, a(n) for n=0..35.

Aoife Hennessy, A Study of Riordan Arrays with Applications to Continued Fractions, Orthogonal Polynomials and Lattice Paths, Ph. D. Thesis, Waterford Institute of Technology, Oct. 2011.

Formula

a(2n-2) = A000699(n), 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 +...
where G(x) = A(x*G(x)) is the o.g.f. of A000085:
G(x) = 1 + x + 2*x^2 + 4*x^3 + 10*x^4 + 26*x^5 + 76*x^6 + 232*x^7 +...
while the e.g.f. of A000085 is given by:
exp(x+x^2/2) = 1 + x + 2*x^2/2! + 4*x^3/3! + 10*x^4/4! + 26*x^5/5! +...

Prog

(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)}

Crossrefs

Cf. A000085, A000699, A172394 (variant).

Sequence in context: A269276 A359521 A172394 * A358653 A270281 A270728

Adjacent sequences: A172392 A172393 A172394 * A172396 A172397 A172398

Keyword

nonn

Author

Paul D. Hanna, Feb 06 2010

Status

approved