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%I #33 May 07 2023 01:22:03
%S 1,11,1573,2716571,56328099685,14016177372718235,
%T 41852067359921313500005,1499635200191700040518673659035,
%U 644815685260091508353787979063721364325,3327107302821620489265827570792988872583047378075
%N a(n) = Product_{i=1..n} (12^i - 1).
%C In general, Product_{i=1..n} (q^i-1) ~ c * q^(n*(n+1)/2), where c = Product_{k >= 1} (1-1/q^k). - _Vaclav Kotesovec_, Nov 21 2015
%H G. C. Greubel, <a href="/A027880/b027880.txt">Table of n, a(n) for n = 0..50</a>
%F a(n) ~ c * 12^(n*(n+1)/2), where c = Product_{k>=1} (1-1/12^k) = 0.909726268905994888636362046977080249120791691941... . - _Vaclav Kotesovec_, Nov 21 2015
%F (11)^n*(13)^(floor(n/2))|a(n) for n>=0. - _G. C. Greubel_, Nov 24 2015
%F Equals 12^(binomial(n+1,2))*(1/12;1/12)_{n}, where (a;q)_{n} is the q-Pochhammer symbol. - _G. C. Greubel_, Dec 24 2015
%F G.f.: Sum_{n>=0} 12^(n*(n+1)/2)*x^n / Product_{k=0..n} (1 + 12^k*x). - _Ilya Gutkovskiy_, May 22 2017
%F Sum_{n>=0} (-1)^n/a(n) = A132268. - _Amiram Eldar_, May 07 2023
%t FoldList[Times,1,12^Range[10]-1] (* _Harvey P. Dale_, Mar 01 2015 *)
%t Abs@QPochhammer[12, 12, Range[0, 30]] (* _G. C. Greubel_, Nov 24 2015 *)
%o (PARI) a(n) = prod(k=1, n, 12^k - 1) \\ _Altug Alkan_, Nov 25 2015
%o (Magma) [1] cat [&*[12^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), A027873 (q=6), A027875 (q=7), A027876 (q=8), A027877 (q=9), A027878 (q=10), A027879 (q=11).
%Y Cf. A132268.
%K nonn
%O 0,2
%A _N. J. A. Sloane_
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