A260776 Certain directed lattice paths.

1, 5, 60, 1001, 19380, 408595, 9104550, 210905400, 5028168132, 122563178210, 3040594338320, 76520801509425, 1948777701739050, 50129821093933224, 1300611345665798320, 33994757853301868560, 894295618431497324900, 23660280955151412585930, 629143806228348421209768

Offset: 0

Author

N. J. A. Sloane, Jul 30 2015

Keywords

• nonn
• easy

Comments

See Dziemianczuk (2014) for precise definition.

Links

• Lars Blomberg, Table of n, a(n) for n = 0..100
• M. Dziemianczuk, On Directed Lattice Paths With Additional Vertical Steps, arXiv preprint arXiv:1410.5747 [math.CO], 2014.

Formula

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

From Peter Bala, Mar 30 2020: (Start)

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

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)

Extensions

More terms from Lars Blomberg, Aug 01 2015