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 A179972 #13 Jul 09 2023 12:08:23 %S A179972 1,1,1,2,1,1,6,2,2,1,1,24,6,6,2,2,1,1,120,24,24,24,6,6,6,2,2,1,1,720, %T A179972 120,120,120,24,24,24,24,6,6,6,2,2,1,1,5040,720,720,720,720,120,120, %U A179972 120,120,120,24,24,24,24,24,6,6,6,2,2,1,1,40320 %N A179972 Irregular table T(n,k) = A178886(n,k)/A048996(n,k) read by rows. %C A179972 Row n has A000041(n) terms. %C A179972 Consider the five partitions of the number 4: %C A179972 4 3+1 2+2 2+1+1 and 1+1+1+1 %C A179972 rewriting as 4000 3100 2200 2110 and 1111 %C A179972 then a(n) counts the ways that the zeros can be permuted: %C A179972 6,2,2,1,1 %C A179972 agreeing with the factorial of the difference between A036042 and A036043. %F A179972 T(n,k) = ( A036042(n,k) - A036043(n,k))!. %F A179972 T(n,k) = n!/A178888(n,k). - _R. J. Mathar_, Mar 03 2011 %e A179972 Row four of A178886 begins: 6 4 2 3 1 %e A179972 Row four of A048996 begins: 1 2 1 3 1 %e A179972 so, %e A179972 Row four of A179972 begins: 6 2 2 1 1 %e A179972 Triangle T(n,k) begins: %e A179972 1; %e A179972 1, 1; %e A179972 2, 1, 1; %e A179972 6, 2, 2, 1, 1; %e A179972 24, 6, 6, 2, 2, 1, 1; %e A179972 120, 24, 24, 24, 6, 6, 6, 2, 2, 1, 1; %e A179972 ... %Y A179972 Cf. A178886, A048996, A036042, A036043, A179973 (row sums). %K A179972 nonn,tabf %O A179972 1,4 %A A179972 _Alford Arnold_, Aug 04 2010