0,4

Hankel transform appears to be a signed aerated version of A059492. - Paul Barry (pbarry(AT)wit.ie), Apr 16 2008

Row sums of inverse Riordan array (1, x(1-x^2))^(-1). - Paul Barry (pbarry(AT)wit.ie), Apr 16 2008

L. W. Beineke and R. E. Pippert, Enumerating dissectable polyhedra by their automorphism groups, Canad. J. Math., 26 (1974), 50-67.

S. J. Cyvin et al., Enumeration of staggered conformers of alkanes: complete solution ..., J. Molec. Struct., 413 (1997), 237-239.

S. J. Cyvin et al., Enumeration of staggered conformers of alkanes..., J. Molec. Struct., 445 (1998), 127-13.

E. Deutsch, Problem 10751, Amer. Math. Monthly, 108 (Nov., 2001), 872-873.

E. Deutsch, S. Feretic and M. Noy, Diagonally convex directed polyominoes and even trees: a bijection and related issues, Discrete Math., 256 (2002), 645-654.

M. Bousquet and C. Lamathe, Enumeration of solid trees according to edge number and edge degree distribution, Discr. Math., 298 (2005), 115-141.

Alexander Burstein, Sergi Elizalde and Toufik Mansour, Restricted Dumont permutations, Dyck paths, and noncrossing partitions, arXiv math.CO/0610234. [Theorem 3.5]

C. Kimberling, Matrix Transformations of Integer Sequences, J. Integer Seqs., Vol. 6, 2003.

G.f. is 1+Z, where Z satisfies x*Z^3 + (3*x-2)*Z^2 + (3*x-1)*Z + x = 0. Equivalently, the g.f. Y satisfies x*Y^3 - 2*Y^2 + 3*Y - 1 = 0. - Vladeta Jovovic (vladeta(AT)Eunet.yu), Dec 06 2002

Reversion of g.f. (x-2x^2)/(1-x)^3 (ignoring signs). - R. Stephan, Mar 22 2004

G.f.: (4/(3x))(sin((1/3)*asin(sqrt(27x^2/4))))^2+(2/sqrt(3x^2))*sin((1/3)*asin(sqrt(27x^2/4))); - Paul Barry (pbarry(AT)wit.ie), Nov 08 2006

G.f.: 1/(1-2*sin(asin(3*sqrt(3)x/2)/3)/sqrt(3)); - Paul Barry (pbarry(AT)wit.ie), Apr 16 2008

A047749 := proc(m) if m mod 2 = 1 then x := (m-1)/2; RETURN((3*x+1)!/((x+1)!*(2*x+1)!)); fi; x := m/2; RETURN((3*x)!/(x!*(2*x+1)!)); end;

A047749 := proc(m) local x; if m mod 2 = 1 then x := (m-1)/2; RETURN((3*x+1)!/((x+1)!*(2*x+1)!)); fi; RETURN(A001764(m/2)); end;

Cf. A001764.

Sequence in context: A130616 A089324 A111759 this_sequence A134565 A100982 A034786

Adjacent sequences: A047746 A047747 A047748 this_sequence A047750 A047751 A047752

nonn

njas