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.
%I A321901 #15 Feb 09 2020 02:42:33
%S A321901 1,1,3,1,3,5,7,1,3,13,7,9,11,5,15,1,19,29,7,25,27,21,15,17,3,13,23,9,
%T A321901 11,5,31,1,19,29,7,57,27,21,15,49,35,13,23,41,43,5,31,33,51,61,39,25,
%U A321901 59,53,47,17,3,45,55,9,11,37,63
%N A321901 Irregular table read by rows: T(n,k) = (2*k+1)^(-(2*k+1)) mod 2^n, 0 <= k <= 2^(n-1) - 1.
%C A321901 The n-th row contains 2^(n-1) numbers, and is a permutation of the odd numbers below 2^n.
%C A321901 For all n, k we have v(T(n,k)-1, 2) = v(k, 2) + 1 and v(T(n,k)+1, 2) = v(k+1, 2) + 1, where v(k, 2) = A007814(k) is the 2-adic valuation of k.
%C A321901 For n >= 3, T(n,k) = 2*k + 1 iff k == -1 (mod 2^floor((n-1)/2)) or k = 0 or k = 2^(n-2).
%C A321901 T(n,k) is the multiplicative inverse of A320561(n,k) modulo 2^n.
%F A321901 T(n,k) = 2^n - A320561(n,2^(n-1)-1-k).
%e A321901 Table starts
%e A321901 1,
%e A321901 1, 3,
%e A321901 1, 3, 5, 7,
%e A321901 1, 3, 13, 7, 9, 11, 5, 15,
%e A321901 1, 19, 29, 7, 25, 27, 21, 15, 17, 3, 13, 23, 9, 11, 5, 31,
%e A321901 1, 19, 29, 7, 57, 27, 21, 15, 49, 35, 13, 23, 41, 43, 5, 31, 33, 51, 61, 39, 25, 59, 53, 47, 17, 3, 45, 55, 9, 11, 37, 63,
%e A321901 ...
%o A321901 (PARI) T(n, k) = lift(Mod(2*k+1, 2^n)^(-(2*k+1)))
%o A321901 tabf(nn) = for(n=1, nn, for(k=0, 2^(n-1)-1, print1(T(n, k), ", ")); print)
%Y A321901 Cf. A007814.
%Y A321901 {x^x} and its inverse: A320561 & A320562.
%Y A321901 {x^(-x)} and its inverse: this sequence & A321904.
%Y A321901 {x^(1/x)} and its inverse: A321902 & A321905.
%Y A321901 {x^(-1/x)} and its inverse: A321903 & A321906.
%K A321901 nonn,tabf
%O A321901 1,3
%A A321901 _Jianing Song_, Nov 21 2018