cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A216787 a(n) = Product_{k=1..n} (144 - 12/k).

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%I A216787 #16 Aug 17 2025 03:50:46
%S A216787 1,132,18216,2550240,359583840,50917071744,7230224187648,
%T A216787 1028757612985344,146597959850411520,20914642271992043520,
%U A216787 2986610916440463814656,426813850967673556058112,61034380688377318516310016,8732611390798600956948971520,1250010944797171165551838494720
%N A216787 a(n) = Product_{k=1..n} (144 - 12/k).
%C A216787 This sequence is generalizable: Product_{k=1..n} (q^2 - q/k) = (q^n/n!) * Product_{k=0..n-1} (q*k + q-1) = expansion of (1- x*q^2)^((1-q)/q).
%F A216787 From _Amiram Eldar_, Aug 17 2025: (Start)
%F A216787 a(n) = 144^n * Gamma(n+11/12) / (Gamma(11/12) * Gamma(n+1)).
%F A216787 a(n) ~ c * 144^n / n^(1/12), where c = 1/Gamma(11/12) = 0.947376... . (End)
%p A216787 seq(product(144-12/k, k=1.. n), n=0..20);
%p A216787 seq((12^n/n!)*product(12*k+11, k=0.. n-1), n=0..20);
%t A216787 Join[{1},FoldList[Times,144-12/Range[20]]] (* _Harvey P. Dale_, Dec 22 2015 *)
%Y A216787 Cf. A004988, A049382, A004994, A216702, A216703, A216704, A216705, A216706, A216786.
%K A216787 nonn
%O A216787 0,2
%A A216787 _Michel Lagneau_, Sep 16 2012