A288539 Number of Dyck paths of semilength n such that at least one positive level has no peaks.

1, 0, 1, 2, 8, 25, 83, 282, 971, 3386, 11940, 42504, 152546, 551426, 2005930, 7337901, 26976726, 99618976, 369349607, 1374391706, 5131186060, 19214759396, 72152791729, 271629133830, 1024989876797, 3876208984221, 14688301498888, 55763768987236, 212077310097784

Offset

0,4

Comments

a(0) = 1 by convention.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..300

Wikipedia, Counting lattice paths

Example

: a(3) = 2:
:                 /\
:        /\/\    /  \
:       /    \  /    \  .

Crossrefs

Column k=0 of A288387.

Cf. A000108.

Sequence in context: A212323 A301842 A240478 * A281338 A036367 A115256

Adjacent sequences: A288536 A288537 A288538 * A288540 A288541 A288542

Keyword

nonn

Author

Alois P. Heinz, Jun 11 2017

Status

approved