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A337902
The number of walks of length 2n+1 on the square lattice that start from the origin (0,0) and end at the vertex (2,1).
4
3, 50, 735, 10584, 152460, 2208492, 32207175, 472780880, 6982113996, 103673813880, 1546866469148, 23179817220000, 348690679038000, 5263441096145400, 79698007774092375, 1210159553338375200, 18422202264818467500, 281089726445607849000
OFFSET
1,1
FORMULA
a(n) = binomial(2*n+1,n-1)*binomial(2*n+1,n) = A002054(n)*A001700(n).
G.f.: 3*x*3F2(2,5/2,5/2; 3,4; 16*x).
D-finite with recurrence (n-1)*(n+2)*(n+1)*a(n) -4*n*(2*n+1)^2*a(n-1)=0.
A135389(n) = 2*A060150(n+1) +2*a(n).
EXAMPLE
a(1)=3 represents 3 walks of length 3: RRU, URR and RUR.
CROSSREFS
Cf. A002894 (at (0,0)), A060150 (at (1,0)), A135389 (at (1,1)), A337900 (at (2,0)), A337901 (at (3,0))
Sequence in context: A034201 A099346 A075184 * A246283 A326250 A308331
KEYWORD
nonn,easy,walk
AUTHOR
R. J. Mathar, Sep 29 2020
STATUS
approved