OFFSET
1,2
COMMENTS
See A208650. The trace of a path is a permutation of (1,2,...,n) if and only if the range of the path is {1,2,...,n}.
LINKS
Nick Early, Generalized Permutohedra, Scattering Amplitudes, and a Cubic Three-Fold, arXiv:1709.03686 [math.CO], 2017.
EXAMPLE
Taking n=3:
row 1: {1},{2},{3} ---------> 1,2,3
row 2: {1,2},{1,3},{2,3} ---> 1,1,2,2,3,3
row 3: {1,2,3} -------------> 1,2,3
3 ways to choose a number from row 1,
4 ways to choose a different number from row 2,
1 way to choose remaining number from row 3.
Total: a(3) = 1*4*3 = 12 paths.
MATHEMATICA
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, Mar 01 2012
STATUS
approved