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 A368028 #23 Dec 23 2023 21:50:17 %S A368028 1,0,1,0,1,1,0,2,1,1,0,6,6,1,1,0,24,54,6,1,1,0,120,648,90,6,1,1,0,720, %T A368028 9720,1944,90,6,1,1,0,5040,174960,52920,2520,90,6,1,1,0,40320,3674160, %U A368028 1730160,99000,2520,90,6,1,1,0,362880,88179840,65998800,4806000,113400,2520,90,6,1,1,0,3628800,2380855680,2877275520,274050000,6966000,113400,2520,90,6,1,1 %N A368028 Square array read by antidiagonals; T(n,k) = number of ways a vehicle with capacity k can transport n distinct individuals with distinct starting and finishing points. %H A368028 math.stackexchange, <a href="https://math.stackexchange.com/a/4832650/6460">Passenger entrance/exit combinations</a> %F A368028 If f(n,k,c)=n*f(n-1,k,c+1)+c*f(n,k,c-1) with f(n,k,c)=0 when n<0 or k<0 or c<0 or k<c and starting with f(0,k,0)=1, then this shows the values of f(n,k,0). %e A368028 T(3,2)=54 represented by the nine patterns AABBCC, AABCBC, AABCCB, ABABCC, ABACBC, ABACCB, ABBACC, ABBCAC, ABBCCA multiplied by 3!=6 for the permutations of A,B,C; but for example ABCABC would not work as the vehicle would be over its capacity of 2 after picking up 3 passengers. %Y A368028 Cf. A080934. Rows include A000012, A057427. Columns include A000007, A000142, A034001. Diagonals include A000680 and A071798. %K A368028 nonn,tabl %O A368028 0,8 %A A368028 _Henry Bottomley_, Dec 24 2023