OFFSET
0,2
COMMENTS
Hankel transform is 9^binomial(n+1,2).
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..500
FORMULA
a(n) = Sum_{k=0..n} A120730(n,k) * 9^k.
MATHEMATICA
a[n_]:= a[n]= If[n==0, 1, If[OddQ[n], 10*a[n-1] -9^((n-1)/2)*CatalanNumber[(n-1)/2], 10*a[n-1] ]];
Table[a[n], {n, 0, 30}] (* G. C. Greubel, Jan 04 2022 *)
PROG
(Sage)
def a(n): # a = A156577
if (n==0): return 1
elif (n%2==1): return 10*a(n-1) - 9^((n-1)/2)*catalan_number((n-1)/2)
else: return 10*a(n-1)
[a(n) for n in (0..30)] # G. C. Greubel, Jan 04 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Philippe Deléham, Feb 10 2009
STATUS
approved