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

0,2

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)

Crossrefs

Sequence in context: A380213 A277300 A156125 * A128574 A120976 A384524

Adjacent sequences: A260773 A260774 A260775 * A260777 A260778 A260779

Keyword

nonn,easy

Author

N. J. A. Sloane, Jul 30 2015

Extensions

More terms from Lars Blomberg, Aug 01 2015

Status

approved