0,2

Number of rooted unlabeled connected triangular maps on a compact closed oriented surface with 2n faces (and thus 3n edges). [Vidal]

Equivalently, the number of pair of permutations (sigma,tau) up to simultaneous conjugacy on a pointed set of size 6*n with sigma^3=tau^2=1, acting transitively and with no fixed point. [Vidal]

Also, the asymptotic expansion of the Airy function Ai'(x)/Ai(x) = -sqrt(x) - 1/(4x) + sum_{n>=2} (-1)^n a(n) (4x)^ (1/2-3n/2). [Praehofer]

Maple 6 gives the wrong asymptotics of Ai'(x)=AiryAi(1,x) as x->infty apart from the 3rd term. Therefore asympt(AiryAi(1,x/4)/AiryAi(x/4),x); reproduces only the value a(1)=1 correctly.

S. Janson, The Wiener index of simply generated random trees, Random Structures Algorithms 22 (2003) 337-358.

Michael J. Kearney, Satya N. Majumdar and Richard J. Martin, The first-passage area for drifted Brownian motion and the moments of the Airy distribution, arXiv:0706.2038. [a(n) = 8^n * K_n from Eq. (3)]

S. R. Finch, Shapes of binary trees

With a(0) = -1/2 one has for n > 0 the recurrence a(n) = (6*n-8)*a(n-1)+sum(a(k)*a(n-k), k=1..n-1) [Praehofer]

Pointed version of A012114. Connected pointed version of A012115.

Cf. A060506, A060507, A094199, A121350, A121352, A005133.

Sequence in context: A156125 A128574 A120976 this_sequence A113665 A147585 A138215

Adjacent sequences: A062977 A062978 A062979 this_sequence A062981 A062982 A062983

nonn,nice,easy

Michael Praehofer (praehofer(AT)ma.tum.de), Jul 24 2001

Entry revised by N. J. A. Sloane (njas(AT)research.att.com) based on comments from Samuel Alexandre Vidal (samuel.vidal(AT)free.fr), Mar 30 2007.