A380243 Number of rooted 2n-regular planar maps with 3 vertices.

1, 54, 3000, 171500, 10001880, 591666768, 35371207872, 2131746903000, 129299660919000, 7883256659941520, 482689850761774656, 29661047546558142624, 1828220386252351000000, 112982297841774018000000, 6998159395715622920640000, 434337846995341921726638000, 27004842919501042631643927000

Offset

1,2

Comments

There are no odd valent regular planar maps with 3 vertices.

Links

Andrew Howroyd, Table of n, a(n) for n = 1..200

Formula

a(n) = n*binomial(2*n-1, n)^3.

a(n) = n*A002897(n - 1).

a(n) ~ 8^(2*n-1) / (sqrt(n) * Pi^(3/2)). - Amiram Eldar, Oct 18 2025

Prog

(PARI) a(n) = n*binomial(2*n-1, n)^3

Crossrefs

Row n=3 of A380241.

Cf. A000984, A002897, A380242.

Sequence in context: A189200 A042405 A187304 * A309422 A212705 A046199

Adjacent sequences: A380240 A380241 A380242 * A380244 A380245 A380246

Keyword

nonn,easy

Author

Andrew Howroyd, Jan 22 2025

Status

approved