0,3

Tha Hankel transform of this sequence is A121835 . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Aug 31 2006

a(n) is the moment of order (n-1) for the discrete measure associated to the weight rho(j+1/2)=2^(j+1/2)/(Pi*binomial(2j+1,j+1/2)), with j integral. So we have a(n)=sum((j+1/2)^(n-1)*rho(j+1/2),j=0..infinity). [From roland groux (roland.groux(AT)orange.fr), Jan 05 2009]

M. Klazar, Twelve countings with rooted plane trees, European Journal of Combinatorics 18 (1997), 195-210; Addendum, 18 (1997), 739-740.

Recurrence : a(n+1) = 1 + sum { j=1, n, (-1+binomial(n+1, j))*a(n) } - Jon Perry (perry(AT)globalnet.co.uk), Apr 25 2005

The Hankel transform of this sequence is A121835 . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Aug 31 2006

E.g.f. A(x) satisfies: A(x) = 1 + integral( A(x)^3 * exp(-x) ). - Paul D. Hanna (pauldhanna(AT)juno.com), Jan 24 2008

(PARI) {a(n)=n!*polcoeff((exp(x +x*O(x^n))/(2-exp(x +x*O(x^n))))^(1/2), n)} (PARI) /* As solution to integral equation: */ {a(n)=local(A=1+x+x*O(x^n)); for(i=0, n, A=1+intformal(A^3*exp(-x+x*O(x^n)))); n!*polcoeff(A, n)} - Paul D. Hanna (pauldhanna(AT)juno.com), Jan 24 2008

Cf. A000110.

Cf. variants: A136727, A136728, A136729.

Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Feb 20 2009: (Start)

Equals row sums of triangle A156920 (row sums (n) = a(n+1))

(End)

Sequence in context: A043546 A080831 A006947 this_sequence A000154 A003713 A058129

Adjacent sequences: A014304 A014305 A014306 this_sequence A014308 A014309 A014310

nonn

N. J. A. Sloane (njas(AT)research.att.com).