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.

A269661 a(n) = Product_{i=1..n} (5^i - 4^i).

This page as a plain text file.
%I A269661 #51 Nov 16 2024 22:15:12
%S A269661 1,9,549,202581,425622681,4907003889249,302963327126122509,
%T A269661 98490045052104040328301,166544794872251942218390753281,
%U A269661 1451779137596368920662880897497387769,64798450159010700654830227323217753649135349
%N A269661 a(n) = Product_{i=1..n} (5^i - 4^i).
%F A269661 a(n) = Product_{i=1..n} A005060(i).
%F A269661 a(n) = 5^(binomial(n+1,2))*(4/5;4/5)_{n}, where (a;q)_{n} is the q-Pochhammer symbol. - _G. C. Greubel_, Mar 05 2016
%F A269661 a(n) ~ c * 5^(n*(n+1)/2), where c = QPochhammer(4/5) = 0.00336800585242312126... . - _Vaclav Kotesovec_, Oct 10 2016
%t A269661 Table[Product[5^i - 4^i, {i, n}], {n, 15}] (* _Vincenzo Librandi_, Mar 03 2016 *)
%t A269661 Table[5^(Binomial[n + 1, 2]) *QPochhammer[4/5, 4/5, n], {n, 1, 20}] (* _G. C. Greubel_, Mar 05 2016 *)
%t A269661 FoldList[Times,Table[5^n-4^n,{n,15}]] (* _Harvey P. Dale_, Aug 28 2018 *)
%o A269661 (Magma) [&*[ 5^k-4^k: k in [1..n] ]: n in [1..16]]; // _Vincenzo Librandi_, Mar 03 2016
%o A269661 (PARI) a(n) = prod(k=1, n, 5^k-4^k); \\ _Michel Marcus_, Mar 05 2016
%Y A269661 Cf. A005060, A109345.
%Y A269661 Cf. sequences of the form Product_{i=1..n}(j^i - 1): A005329 (j=2), A027871 (j=3), A027637 (j=4), A027872 (j=5), A027873 (j=6), A027875 (j=7), A027876 (j=8), A027877 (j=9), A027878 (j=10), A027879 (j=11), A027880 (j=12).
%Y A269661 Cf. sequences of the form Product_{i=1..n}(j^i - k^1), k>1: A263394 (j=3, k=2), A269576 (j=4, k=3).
%K A269661 nonn,easy
%O A269661 1,2
%A A269661 _Bob Selcoe_, Mar 02 2016