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 A346905 #11 Apr 18 2022 12:29:55
%S A346905 1,2,1,4,6,1,8,28,6,1,16,120,36,8,1,32,496,200,40,10,1,64,2016,1120,
%T A346905 280,60,12,1,128,8128,6272,2240,280,84,14,1,256,32640,35392,15232,
%U A346905 2800,448,112,16,1,512,130816,200832,103936,34272,2016,672,144,18,1
%N A346905 Triangle read by rows: T(n,k) is the number of ways of choosing a k-dimensional cube from the vertices of an n-dimensional hypercube; 0 <= k <= n.
%F A346905 T(n,0) = 2^n.
%F A346905 T(n,k) = 2^(n-k) * Sum_{i=1..floor(n/k)} n!/(k!*(i!)^k*(n-i*k)!).
%F A346905 T(n,k) = 2^(n-k) * A346906(n,k).
%e A346905 Table begins:
%e A346905 n\k | 0 1 2 3 4 5 6 7 8 9
%e A346905 ----+----------------------------------------------------------
%e A346905 0 | 1;
%e A346905 1 | 2, 1;
%e A346905 2 | 4, 6, 1;
%e A346905 3 | 8, 28, 6, 1;
%e A346905 4 | 16, 120, 36, 8, 1;
%e A346905 5 | 32, 496, 200, 40, 10, 1;
%e A346905 6 | 64, 2016, 1120, 280, 60, 12, 1;
%e A346905 7 | 128, 8128, 6272, 2240, 280, 84, 14, 1;
%e A346905 8 | 256, 32640, 35392, 15232, 2800, 448, 112, 16, 1;
%e A346905 9 | 512, 130816, 200832, 103936, 34272, 2016, 672, 144, 18, 1
%e A346905 One of the T(7,3) = 2240 ways of choosing a 3-cube from the vertices of a 7-cube is the cube with the following eight points:
%e A346905 (0,0,0,1,1,1,0);
%e A346905 (1,1,0,1,1,1,0);
%e A346905 (0,0,1,1,1,0,0);
%e A346905 (0,0,0,1,0,1,1);
%e A346905 (1,1,1,1,1,0,0);
%e A346905 (1,1,0,1,0,1,1);
%e A346905 (0,0,1,1,0,0,1); and
%e A346905 (1,1,1,1,0,0,1).
%t A346905 T[n_, 0] := 2^n
%t A346905 T[n_, k_] := 2^(n - k)*Sum[n!/(k!*(i!)^k*(n - i*k)!), {i, 1, n/k}]
%Y A346905 Columns: A000079 (k=0), A006516 (k=1), A345340 (k=2).
%Y A346905 Cf. A346906.
%K A346905 nonn,tabl
%O A346905 0,2
%A A346905 _Peter Kagey_, Aug 06 2021