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.

A323545 a(n) = Product_{k=0..n} (k^7 + (n-k)^7).

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%I A323545 #17 Sep 08 2022 08:46:23
%S A323545 0,1,32768,79593387129,328983774635229184,8781626117710113525390625,
%T A323545 570409595340477623191338982834176,
%U A323545 112244673425189306235795780017831813874289,49449149324106963036650868175987491957290049732608,48527312221741371319651099141827554314119977393170380398241
%N A323545 a(n) = Product_{k=0..n} (k^7 + (n-k)^7).
%H A323545 Seiichi Manyama, <a href="/A323545/b323545.txt">Table of n, a(n) for n = 0..79</a>
%F A323545 a(n) ~ exp((8*cos((Pi + arctan(2769*sqrt(3)/239))/6)*Pi/sqrt(21)-6)*n) * n^(7*n+7).
%F A323545 Equivalently, a(n) ~ exp((4*Pi*sqrt(2*(13 + 19*sin(Pi/14) - sin(3*Pi/14))/7)/7 - 6)*n) * n^(7*n+7). - _Vaclav Kotesovec_, Jan 23 2019
%t A323545 Table[Product[k^7+(n-k)^7, {k, 0, n}], {n, 0, 10}]
%o A323545 (PARI) m=7; vector(10, n, n--; prod(k=0,n, k^m + (n-k)^m)) \\ _G. C. Greubel_, Jan 18 2019
%o A323545 (Magma) m:=7; [(&*[k^m + (n-k)^m: k in [0..n]]): n in [0..10]]; // _G. C. Greubel_, Jan 18 2019
%o A323545 (Sage) m=7; [product(k^m +(n-k)^m for k in (0..n)) for n in (0..10)] # _G. C. Greubel_, Jan 18 2019
%Y A323545 Cf. A323535, A323540, A323541, A323542, A323543, A323544, A323546, A320345.
%Y A323545 Cf. 2*A000541 (with sum instead of product).
%K A323545 nonn
%O A323545 0,3
%A A323545 _Vaclav Kotesovec_, Jan 17 2019