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A337351 a(n) is the number of lattice paths from (0,0) to (3n,2n) using only the steps (1,0) and (0,1) and which do not touch any other points of the form (3k,2k). 2
1, 10, 110, 1805, 34770, 731760, 16295600, 377438250, 8999246900, 219399101415, 5444124108810, 137040309706725, 3490834454580950, 89816746611096280, 2330761164942308080, 60932036847971297230, 1603218808449019802550, 42423276620326253035205 (list; graph; refs; listen; history; text; internal format)
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(5*n,2*n) * x^n).
PROG
(PARI) seq(n)={Vec(2 - 1/(O(x*x^n) + sum(k=0, n, binomial(5*k, 2*k)*x^k)))} \\ Andrew Howroyd, Aug 25 2020
CROSSREFS
Sequence in context: A055530 A108487 A099883 * A146753 A297500 A305213
KEYWORD
nonn,easy
AUTHOR
Lucas A. Brown, Aug 24 2020
STATUS
approved

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Last modified February 22 06:21 EST 2024. Contains 370240 sequences. (Running on oeis4.)