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A135389 Number of walks from origin to (1,1) in a square lattice. 2
2, 24, 300, 3920, 52920, 731808, 10306296, 147232800, 2127513960, 31031617760, 456164781072, 6749962774464, 100445874620000, 1502052155856000, 22557604697766000, 340044833169460800, 5143178101688094600 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

a(n) is the number of walks of length 2n+2 in an infinite square lattice that begin at the origin and end at (1,1) using steps (1,0), (-1,0), (0,1), (0,-1).

LINKS

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

S. Hollos and R. Hollos, Lattice Paths and Walks.

FORMULA

a(n) = binomial(2n+2,n) * binomial(2n+2,n+1).

n*(n+2)*a(n) -4*(2*n+1)^2*a(n-1)=0. - R. J. Mathar, Jul 14 2013

E.g.f.: Sum_{n>0} a(n-1) * x^(2*n)/(2*n)! = BesselI(1, 2*x)^2. - Michael Somos, Oct 17 2019

EXAMPLE

G.f. = 2 + 24*x + 300*x^2 + 3920*x^3 + 731808*x^4 + 10306296*x^5 + ... - Michael Somos, Oct 17 2019

MAPLE

series( 2*hypergeom([3/2, 3/2], [3], 16*x), x=0, 20);  # Mark van Hoeij, Apr 06 2013

MATHEMATICA

Table[Binomial[2n + 2, n] Binomial[2n + 2, n + 1], {n, 0, 19}] (* Alonso del Arte, Apr 06 2013 *)

CROSSREFS

Cf. A002894, A060150.

Sequence in context: A230129 A065101 A052739 * A065513 A246190 A246610

Adjacent sequences:  A135386 A135387 A135388 * A135390 A135391 A135392

KEYWORD

easy,nonn

AUTHOR

Stefan Hollos (stefan(AT)exstrom.com), Dec 11 2007

STATUS

approved

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Last modified November 17 23:26 EST 2019. Contains 329242 sequences. (Running on oeis4.)