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%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
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