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 A328718 #35 Oct 30 2019 08:28:33 %S A328718 1,1,1,1,1,1,1,3,1,1,1,7,5,1,1,1,19,13,7,1,1,1,51,61,19,9,1,1,1,141, %T A328718 221,127,25,11,1,1,1,393,1001,511,217,31,13,1,1,1,1107,4145,3301,921, %U A328718 331,37,15,1,1,1,3139,18733,16297,7761,1451,469,43,17,1,1 %N A328718 Square array T(n,k), n>=0, k>=0, read by antidiagonals, where T(n,k) is the constant term in the expansion of (1 + x_1 + x_2 + ... + x_n + 1/x_1 + 1/x_2 + ... + 1/x_n)^k. %C A328718 T(n,k) is the number of k-step closed walks (from origin to origin) in n-dimensional lattice where each step changes at most one component by -1 or by +1. - _Alois P. Heinz_, Oct 26 2019 %C A328718 Conjecture: Row r is asymptotic to (2*r+1)^(n + r/2) / (2^r * (Pi*n)^(r/2)). - _Vaclav Kotesovec_, Oct 27 2019 %H A328718 Alois P. Heinz, <a href="/A328718/b328718.txt">Antidiagonals n = 0..140, flattened</a> %F A328718 From _Vaclav Kotesovec_, Oct 30 2019: (Start) %F A328718 Columns: %F A328718 T(n,2) = 2*n + 1. %F A328718 T(n,3) = 6*n + 1. %F A328718 T(n,4) = 12*n^2 + 6*n + 1. %F A328718 T(n,5) = 60*n^2 - 10*n + 1. %F A328718 T(n,6) = 120*n^3 + 20*n + 1. %F A328718 T(n,7) = 840*n^3 - 840*n^2 + 392*n + 1. (End) %e A328718 Square array begins: %e A328718 1, 1, 1, 1, 1, 1, 1, 1, ... %e A328718 1, 1, 3, 7, 19, 51, 141, 393, ... %e A328718 1, 1, 5, 13, 61, 221, 1001, 4145, ... %e A328718 1, 1, 7, 19, 127, 511, 3301, 16297, ... %e A328718 1, 1, 9, 25, 217, 921, 7761, 41889, ... %e A328718 1, 1, 11, 31, 331, 1451, 15101, 85961, ... %e A328718 1, 1, 13, 37, 469, 2101, 26041, 153553, ... %Y A328718 Rows n=0-5 give A000012, A002426, A201805, A328713, A328714, A328715. %Y A328718 Main diagonal is A328716. %K A328718 nonn,tabl %O A328718 0,8 %A A328718 _Seiichi Manyama_, Oct 26 2019