OFFSET
0,2
COMMENTS
The number of paths of odd length 2*j+1 is the same as the number of even length 2*j (returning to 0 exactly k times).
LINKS
Muniru A Asiru, Table of n, a(n) for n = 0..1325
FORMULA
EXAMPLE
Triangle T(j,k) begins:
1
2, 2
6, 6, 4
20, 20, 16, 8
70, 70, 60, 40, 16
252, 252, 224, 168, 96, 32
924, 924, 840, 672, 448, 224, 64
3432, 3432, 3168, 2640, 1920, 1152, 512, 128
12870, 12870, 12012, 10296, 7920, 5280, 2880, 1152, 256
48620, 48620, 45760, 40040, 32032, 22880, 14080, 7040, 2560, 512
PROG
(GAP) Flat(List([0..10], j->List([0..j], k->2^k*Binomial(2*j-k, j-k)))); # Muniru A Asiru, May 18 2018
CROSSREFS
KEYWORD
AUTHOR
Franz Vrabec, Sep 27 2016
STATUS
approved