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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).
2
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
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
KEYWORD
nonn,easy
AUTHOR
Lucas A. Brown, Aug 24 2020
STATUS
approved