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 A383905 #14 May 26 2025 17:48:15 %S A383905 1,0,1,0,1,1,0,1,3,1,0,1,6,7,1,0,1,10,28,15,1,0,1,15,84,120,31,1,0,1, %T A383905 21,210,680,496,63,1,0,1,28,462,3060,5456,2016,127,1,0,1,36,924,11628, %U A383905 46376,43680,8128,255,1,0,1,45,1716,38760,324632,720720,349504,32640,511,1 %N A383905 Square table read by descending antidiagonals where T(n,k) = binomial(k+2^n-2,k). %C A383905 T(n,k) is the number of right total relations between a set of n distinguishable elements and a set of k indistinguishable elements. %e A383905 Rows start: %e A383905 1, 0, 0, 0, 0, ... %e A383905 1, 1, 1, 1, 1, ... %e A383905 1, 3, 6, 10, 15, ... %e A383905 1, 7, 28, 84, 210, ... %e A383905 1, 15, 120, 680, 3060, ... %p A383905 T:= (n, k)-> binomial(k+2^n-2, k): %p A383905 seq(seq(T(n, d-n), n=0..d), d=0..10); # _Alois P. Heinz_, May 16 2025 %Y A383905 Cf. A383902 (ascending diagonals), A137153 (no restriction on totality). %K A383905 nonn,tabl %O A383905 0,9 %A A383905 _Isaac R. Browne_, May 15 2025