[go: up one dir, main page]

login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A156577
a(2*n+2) = 10*a(2*n+1), a(2*n+1) = 10*a(2*n) - 9^n*A000108(n), a(0) = 1.
3
1, 9, 90, 891, 8910, 88938, 889380, 8890155, 88901550, 888923646, 8889236460, 88889884542, 888898845420, 8888918303988, 88889183039880, 888889778505099, 8888897785050990, 88888916293698870, 888889162936988700
OFFSET
0,2
COMMENTS
Hankel transform is 9^binomial(n+1,2).
LINKS
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
KEYWORD
nonn
AUTHOR
Philippe Deléham, Feb 10 2009
STATUS
approved