OFFSET
0,3
COMMENTS
Essentially the number of paths starting at the origin, consisting of n U or D steps or starting at the horizontal axis afresh after any number of steps, and never descending below the horizontal axis.
FORMULA
G.f.: 1/(1-g037952(x)) where g037952(x) = x +x^2 + 3*x^3+.. is the g.f. of A037952.
D-finite with recurrence n*a(n) +(-3*n+2)*a(n-1) +(-3*n+8)*a(n-2) +(11*n-46)*a(n-3) +2*(-n+12)*a(n-4) +4*(n-1)*a(n-5) +8*(-n+5)*a(n-6)=0.
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
R. J. Mathar, Sep 24 2021
STATUS
approved