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 A383902 #18 May 26 2025 17:48:56 %S A383902 1,1,0,1,1,0,1,3,1,0,1,7,6,1,0,1,15,28,10,1,0,1,31,120,84,15,1,0,1,63, %T A383902 496,680,210,21,1,0,1,127,2016,5456,3060,462,28,1,0,1,255,8128,43680, %U A383902 46376,11628,924,36,1,0,1,511,32640,349504,720720,324632,38760,1716,45,1,0 %N A383902 Square table read by ascending antidiagonals where T(n,k) = binomial(k+2^n-2,k). %C A383902 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 A383902 Rows start: %e A383902 1, 0, 0, 0, 0, ... %e A383902 1, 1, 1, 1, 1, ... %e A383902 1, 3, 6, 10, 15, ... %e A383902 1, 7, 28, 84, 210, ... %e A383902 1, 15, 120, 680, 3060, ... %p A383902 T:= (n, k)-> binomial(k+2^n-2, k): %p A383902 seq(seq(T(d-k, k), k=0..d), d=0..10); # _Alois P. Heinz_, May 16 2025 %Y A383902 Cf. A383905 (descending diagonals), A092056 (no restriction on totality) %K A383902 nonn,tabl %O A383902 0,8 %A A383902 _Isaac R. Browne_, May 15 2025