A337352 a(n) is the number of lattice paths from (0,0) to (3n,3n) using only the steps (1,0) and (0,1) and which do not touch any other points of the form (3k,3k).

1, 20, 524, 19660, 854380, 40304080, 2004409236, 103440770760, 5486614131756, 297239307415792, 16376472734974384, 914734188877259884, 51680064605716043636, 2948046519564292501232, 169560941932509940657016, 9822377923336683964009296, 572554753384166308597716396

Offset

0,2

Comments

The terms of this sequence may be computed via a determinant; see Lemma 10.7.2 of the Krattenthaler reference for details.

Links

Table of n, a(n) for n=0..16.

Christian Krattenthaler, "Lattice path enumeration". In: Handbook of Enumerative Combinatorics. Edited by Miklos Bona. CRC Press, 2015, pages 589-678.

Formula

G.f.: 2 - 1 / (Sum_{n>=0} binomial(6*n,3*n) * x^n).

Prog

(PARI) seq(n)={Vec(2 - 1/(O(x*x^n) + sum(k=0, n, binomial(6*k, 3*k)*x^k)))} \\ Andrew Howroyd, Aug 25 2020

Crossrefs

Cf. A337291, A337292, A337350, A337351.

Sequence in context: A130033 A250016 A371017 * A180882 A202920 A210486

Adjacent sequences: A337349 A337350 A337351 * A337353 A337354 A337355

Keyword

nonn,easy

Author

Lucas A. Brown, Aug 24 2020

Status

approved