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%I #45 May 07 2023 06:32:11
%S 1,5,175,37625,48724375,378832015625,17674407688984375,
%T 4947685316415841015625,8310206472731792807458984375,
%U 83747726219216824716765369541015625
%N a(n) = Product_{i=1..n} (6^i - 1).
%H G. C. Greubel, <a href="/A027873/b027873.txt">Table of n, a(n) for n = 0..50</a>
%F 5^n|a(n) for n>=0. - _G. C. Greubel_, Nov 20 2015
%F a(n) ~ c * 6^(n*(n+1)/2), where c = Product_{k>=1} (1-1/6^k) = A132034 = 0.805687728162164940923750215496298968917997628693... . - _Vaclav Kotesovec_, Nov 21 2015
%F a(n) = 6^(binomial(n+1,2))*(1/6;1/6)_{n}, where (a;q)_{n} is the q-Pochhammer symbol. - _G. C. Greubel_, Dec 24 2015
%F a(n) = Product_{i=1..n} A024062(i). - _Michel Marcus_, Dec 27 2015
%F G.f.: Sum_{n>=0} 6^(n*(n+1)/2)*x^n / Product_{k=0..n} (1 + 6^k*x). - _Ilya Gutkovskiy_, May 22 2017
%F Sum_{n>=0} (-1)^n/a(n) = A132034. - _Amiram Eldar_, May 07 2023
%t Table[Product[(6^k-1),{k,1,n}],{n,0,20}] (* _Vaclav Kotesovec_, Jul 17 2015 *)
%t Abs@QPochhammer[6, 6, Range[0, 10]] (* _Vladimir Reshetnikov_, Nov 20 2015 *)
%t FoldList[Times,Join[{1},6^Range[10]-1]] (* _Harvey P. Dale_, Oct 13 2017 *)
%o (PARI) a(n) = prod(i=1, n, 6^i-1); \\ _Michel Marcus_, Nov 21 2015
%o (Magma) [1] cat [&*[ 6^k-1: k in [1..n] ]: n in [1..11]]; // _Vincenzo Librandi_, Dec 24 2015
%Y Cf. A005329 (q=2), A027871 (q=3), A027637 (q=4), A027872 (q=5), A027875 (q=7), A027876 (q=8), A027877 (q=9), A027878 (q=10), A027879 (q=11), A027880 (q=12).
%Y Cf. A132034.
%K nonn
%O 0,2
%A _N. J. A. Sloane_
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