OFFSET
0,3
COMMENTS
See Dershowitz (2017) for precise definition.
LINKS
Nachum Dershowitz, Touchard's Drunkard, Journal of Integer Sequences, Vol. 20 (2017), #17.1.5.
FORMULA
From Mélika Tebni, Dec 03 2024: (Start)
Inverse binomial transform of A302184. (End)
Conjecture D-finite with recurrence (n+2)^2*a(n) +(-3*n^2-5*n-1)*a(n-1) -(13*n+15)*(n-1)*a(n-2) +15*(n-1)*(n-2)*a(n-3)=0. - R. J. Mathar, Oct 29 2025
PROG
(Python)
from math import comb as binomial
def M(n): return sum(binomial(n, 2*k)*binomial(2*k, k)//(k+1) for k in range(n//2+1)) # Motzkin numbers
def a(n):
return sum(binomial(n, k)*binomial(k, k//2)*((k+1) %2)*M(n-k) for k in range(n+1))
print([a(n) for n in range(27)]) # Mélika Tebni, Dec 03 2024
CROSSREFS
KEYWORD
nonn,walk
AUTHOR
N. J. A. Sloane, Apr 09 2018
EXTENSIONS
a(13)-a(26) from Mélika Tebni, Dec 03 2024
STATUS
approved
