A337351 - OEIS

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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).

1, 10, 110, 1805, 34770, 731760, 16295600, 377438250, 8999246900, 219399101415, 5444124108810, 137040309706725, 3490834454580950, 89816746611096280, 2330761164942308080, 60932036847971297230, 1603218808449019802550, 42423276620326253035205

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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..17.

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

Cf. A337291, A337292, A337350, A337352.

Sequence in context: A055530 A108487 A099883 * A146753 A297500 A305213

Adjacent sequences: A337348 A337349 A337350 * A337352 A337353 A337354

KEYWORD

nonn,easy

AUTHOR

Lucas A. Brown, Aug 24 2020

STATUS

approved