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.

A128542 a(n) = ((2n)^(2n) - 1)/((2n+1)*(2n-1)).

This page as a plain text file.
%I A128542 #10 Sep 08 2022 08:45:30
%S A128542 0,1,17,1333,266305,101010101,62350352785,56984650387477,
%T A128542 72340172838076673,121815504877079063701,262801002506265664160401,
%U A128542 706890015246831381773595701,2319540481478754999041880822337,9120177155862455275254332279111413
%N A128542 a(n) = ((2n)^(2n) - 1)/((2n+1)*(2n-1)).
%C A128542 p divides a(p-1) for prime p>3.
%H A128542 G. C. Greubel, <a href="/A128542/b128542.txt">Table of n, a(n) for n = 0..190</a>
%F A128542 a(n) = ((2n)^(2n)-1)/((2n+1)*(2n-1)).
%F A128542 a(n) = A048861(2n)/((2n+1)*(2n-1)).
%F A128542 a(n) = A023037(2n)/(2n+1).
%F A128542 a(n) = A089815(2n-2).
%t A128542 Join[{0}, Table[((2n)^(2n)-1)/(4n^2-1),{n,1,20}]]
%o A128542 (PARI) A128542(n)=((n+=n)^n-1)/(n^2-1) \\ _M. F. Hasler_, Oct 31 2014
%o A128542 (Magma) [0] cat [((2*n)^(2*n)-1)/(4*n^2 -1): n in [1..20]]; // _G. C. Greubel_, Jul 11 2019
%o A128542 (Sage) [0]+[((2*n)^(2*n)-1)/(4*n^2 -1) for n in (1..20)] # _G. C. Greubel_, Jul 11 2019
%o A128542 (GAP) Concatenation([0], List([1..20], n-> ((2*n)^(2*n)-1)/(4*n^2 -1) )); # _G. C. Greubel_, Jul 11 2019
%Y A128542 Cf. A048861 = n^n - 1.
%Y A128542 Cf. A023037, A089815.
%K A128542 nonn
%O A128542 0,3
%A A128542 _Alexander Adamchuk_, May 08 2007
%E A128542 a(0)=0 added by _M. F. Hasler_, Oct 31 2014