A027877 - OEIS

%I #36 May 07 2023 01:23:17

%S 1,8,640,465920,3056435200,180476385689600,95912370410881024000,

%T 458745798479390789599232000,19747501938318761090457052119040000,

%U 7650586837724400321220283274999910891520000

%N a(n) = Product_{i=1..n} (9^i - 1).

%H G. C. Greubel, <a href="/A027877/b027877.txt">Table of n, a(n) for n = 0..40</a>

%F a(n) ~ c * 3^(n*(n+1)), where c = Product_{k>=1} (1-1/9^k) = A132037 = 0.876560354035964205836019838417862010106635101174... . - _Vaclav Kotesovec_, Nov 21 2015

%F From  - _G. C. Greubel_, Dec 24 2015: (Start)

%F 8^n * 10^(floor(n/2))|a(n), for n>=0.

%F a(n) = 9^(binomial(n+1,2))*(1/9;1/9)_{n}, where (a;q)_{n} is the q-Pochhammer symbol. (End)

%F a(n) = Product_{i=1..n} A024101(i). - _Michel Marcus_, Dec 27 2015

%F 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

%F Sum_{n>=0} (-1)^n/a(n) = A132037. - _Amiram Eldar_, May 07 2023

%t Abs@QPochhammer[9, 9, Range[0, 10]] (* _Vladimir Reshetnikov_, Nov 20 2015 *)

%o (Magma) [1] cat [&*[ 9^k-1: k in [1..n] ]: n in [1..11]]; // _Vincenzo Librandi_, Dec 24 2015

%o (PARI) a(n) = prod(i=1, n, 9^i-1); \\ _Altug Alkan_, Dec 24 2015

%Y Cf. A005329 (q=2), A027871 (q=3), A027637 (q=4), A027872 (q=5), A027873 (q=6), A027875 (q=7), A027876 (q=8), A027878 (q=10), A027879 (q=11), A027880 (q=12).

%Y Cf. A132037.

%K nonn

%O 0,2

%A _N. J. A. Sloane_