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 A355997 #20 Aug 06 2022 08:06:50
%S A355997 1,0,4,0,1,32,0,0,48,400,0,0,28,1728,6912,0,0,8,4240,62720,153664,0,0,
%T A355997 1,7272,344320,2457600,4194304,0,0,0,8720,1465600,23872320,105815808,
%U A355997 136048896,0,0,0,7136,5254576,182691200,1603840000,5017600000,512000000
%N A355997 Triangle read by rows: T(n,d) is the number of fixed orthoplex n-ominoes with cell centers determining d-space.
%C A355997 Orthoplex polyominoes are connected sets of cells of regular tilings with Schläfli symbols {}, {4}, {3,4}, {3,3,4}, {3,3,3,4}, etc. These are tilings of regular orthoplexes projected on their circumspheres. Orthoplex polyominoes are equivalent to multidimensional polyominoes that do not extend more than two units along any axis, i.e., fit within a 2^d cube. Two fixed polyominoes are identical only if one is a translation of the other.
%C A355997 Conjecture: T(n,n-4) = 2^(n-7) * n^(n-9) * (n-4) * (n-5) * (n-6) * (n^6-14*n^5+65*n^4-189*n^3+594*n^2-1305*n+6832) / 6 ~ A259015(n) / 8.
%H A355997 Robert A. Russell, <a href="/A355997/b355997.txt">Table of n, a(n) for n = 2..73</a>
%e A355997 Triangle begins with T(2,1):
%e A355997 n\d 1 2 3 4 5 6 7 8 9
%e A355997 2 1
%e A355997 3 0 4
%e A355997 4 0 1 32
%e A355997 5 0 0 48 400
%e A355997 6 0 0 28 1728 6912
%e A355997 7 0 0 8 4240 62720 153664
%e A355997 8 0 0 1 7272 344320 2457600 4194304
%e A355997 9 0 0 0 8720 1465600 23872320 105815808 136048896
%e A355997 10 0 0 0 7136 5254576 182691200 1603840000 5017600000 512000000
%Y A355997 Cf. A195739 (multidimensional).
%Y A355997 Diagonals (with formulas) are A127670, A355998, A355999.
%K A355997 nonn,tabl
%O A355997 2,3
%A A355997 _Robert A. Russell_, Jul 22 2022