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A108430 Number of d steps in all paths from (0,0) to (3n,0) that stay in the first quadrant (but may touch the horizontal axis), consisting of steps u=(2,1), U=(1,2), or d=(1,-1). 1

%I

%S 3,31,311,3151,32299,334335,3488239,36627487,386618387,4098713631,

%T 43611791783,465496885231,4981942135611,53443871159551,

%U 574500093677535,6186886528903231,66735614131858723,720897596248427295

%N Number of d steps in all paths from (0,0) to (3n,0) that stay in the first quadrant (but may touch the horizontal axis), consisting of steps u=(2,1), U=(1,2), or d=(1,-1).

%H Emeric Deutsch, <a href="http://www.jstor.org/stable/2589192">Problem 10658: Another Type of Lattice Path</a>, American Math. Monthly, 107, 2000, 368-370.

%F a(n) = (1/n)*sum(k*binomial(n,2n-k)*binomial(n+k,n-1), k=n..2n).

%e a(1) = 3 because in the paths ud, Udd we have 3 d steps altogether.

%p a:=n->(1/n)*sum(k*binomial(n,2*n-k)*binomial(n+k,n-1),k=n..2*n): seq(a(n),n=1..22);

%Y Cf. A027307, A108429.

%K nonn

%O 1,1

%A _Emeric Deutsch_, Jun 03 2005

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Last modified October 19 04:40 EDT 2019. Contains 328211 sequences. (Running on oeis4.)