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%I #36 Jul 27 2024 09:40:21
%S 2,24,200,1400,8820,51744,288288,1544400,8022300,40646320,201753552,
%T 984312784,4732273000,22465296000,105479913600,490481598240,
%U 2261264427180,10345654242000,47009200854000,212283654382800,953254695633240,4258696302569280,18936890673480000
%N Number of one-sided prudent walks from (0,0) to (n,n), with 3+n east steps, 3 west steps and n north steps.
%H Georg Fischer, <a href="/A189769/b189769.txt">Table of n, a(n) for n = 1..170</a> [First 44 terms from _Vincenzo Librandi_]
%H S. Gao and H. Niederhausen, <a href="http://math.fau.edu/Niederhausen/HTML/Papers/Sequences%20Arising%20From%20Prudent%20Self-Avoiding%20Walks-February%2001-2010.pdf">Sequences Arising From Prudent Self-Avoiding Walks</a>, 2010.
%F a(n) = (n+1)*(2+n)*Gamma(2*n)/(3*(Gamma(n)^2).
%t Table[(n+1)*(2+n) Gamma[2*n]/(3 (Gamma[n])^2), {n, 30}] (* _T. D. Noe_, Apr 29 2011 *)
%o (Magma) [ Round((n+1)*(n+2)*Gamma(2*n)/(3*Gamma(n)^2)): n in [1..23] ]; // _Klaus Brockhaus_, Apr 29 2011
%K nonn,walk
%O 1,1
%A _Shanzhen Gao_, Apr 26 2011
%E Extended by _T. D. Noe_, Apr 29 2011
%E a(45) and following corrected by _Georg Fischer_, Jul 27 2024
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