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Certain directed lattice paths.
2

%I #15 Apr 02 2020 11:46:40

%S 1,5,60,1001,19380,408595,9104550,210905400,5028168132,122563178210,

%T 3040594338320,76520801509425,1948777701739050,50129821093933224,

%U 1300611345665798320,33994757853301868560,894295618431497324900,23660280955151412585930,629143806228348421209768

%N Certain directed lattice paths.

%C See Dziemianczuk (2014) for precise definition.

%H Lars Blomberg, <a href="/A260776/b260776.txt">Table of n, a(n) for n = 0..100</a>

%H M. Dziemianczuk, <a href="http://arxiv.org/abs/1410.5747">On Directed Lattice Paths With Additional Vertical Steps</a>, arXiv preprint arXiv:1410.5747 [math.CO], 2014.

%F See Dziemianczuk (2014) Equation (36b) with N=3.

%F From _Peter Bala_, Mar 30 2020: (Start)

%F a(n) = (1/n)*C(5*n,2*n-1) for n >= 1.

%F a(n) = 2*Sum_{k = 0..n} C(3*n+k,n+3*k)*C(n+3*k,k)/(n+2*k+1). Cf. A027307(n) = Sum_{k = 0..n} C(2*n+k,n+2*k)*C(n+2*k,k)/(n+k+1) for n >= 1. (End)

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_, Jul 30 2015

%E More terms from _Lars Blomberg_, Aug 01 2015