OFFSET
0,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..40
FORMULA
a(n) ~ c * 3^(n*(n+1)), where c = Product_{k>=1} (1-1/9^k) = A132037 = 0.876560354035964205836019838417862010106635101174... . - Vaclav Kotesovec, Nov 21 2015
From - G. C. Greubel, Dec 24 2015: (Start)
8^n * 10^(floor(n/2))|a(n), for n>=0.
a(n) = 9^(binomial(n+1,2))*(1/9;1/9)_{n}, where (a;q)_{n} is the q-Pochhammer symbol. (End)
a(n) = Product_{i=1..n} A024101(i). - Michel Marcus, Dec 27 2015
G.f.: Sum_{n>=0} 9^(n*(n+1)/2)*x^n / Product_{k=0..n} (1 + 9^k*x). - Ilya Gutkovskiy, May 22 2017
Sum_{n>=0} (-1)^n/a(n) = A132037. - Amiram Eldar, May 07 2023
MATHEMATICA
Abs@QPochhammer[9, 9, Range[0, 10]] (* Vladimir Reshetnikov, Nov 20 2015 *)
PROG
(Magma) [1] cat [&*[ 9^k-1: k in [1..n] ]: n in [1..11]]; // Vincenzo Librandi, Dec 24 2015
(PARI) a(n) = prod(i=1, n, 9^i-1); \\ Altug Alkan, Dec 24 2015
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved