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 A178803 #18 Feb 25 2020 16:30:16 %S A178803 1,1,2,1,2,6,1,2,2,6,24,1,2,2,6,6,24,120,1,2,2,2,6,6,6,24,24,120,720, %T A178803 1,2,2,2,6,6,6,6,24,24,24,120,120,720,5040,1,2,2,2,2,6,6,6,6,6,24,24, %U A178803 24,24,24,120,120,120,720,720,5040,40320,1,2,2,2,2,6,6,6,6,6,6,6,24,24,24,24,24 %N A178803 Write the factorial of each term in A036043(n). %C A178803 Sequence A036043 measures the length of numeric partitions. %e A178803 A036043 begins 1 1 2 1 2 3 1 2 2 3 4 1 2 2 3 3 4 5 ... %e A178803 so this table begins 1 1 2 1 2 6 1 2 2 6 24 ... %e A178803 1; %e A178803 1, 2; %e A178803 1, 2, 6; %e A178803 1, 2, 2, 6, 24; %e A178803 1, 2, 2, 6, 6, 24, 120; %e A178803 1, 2, 2, 2, 6, 6, 6, 24, 24, 120, 720; %e A178803 1, 2, 2, 2, 6, 6, 6, 6, 24, 24, 24, 120, 120, 720, 5040; %e A178803 1, 2, 2, 2, 2, 6, 6, 6, 6, 6, 24, 24, 24, 24, 24, 120, 120, 120, 720, 720, 5040, 40320; %o A178803 (SageMath) %o A178803 def A178803_row(n): %o A178803 return [factorial(len(p)) for k in (0..n) for p in Partitions(n, length=k)] %o A178803 for n in (0..10): print(A178803_row(n)) # _Peter Luschny_, Nov 02 2019 %Y A178803 Cf. A000041 (shape sequence), A000142 (factorials), A036043, A101880 (row sums). %K A178803 easy,nonn,tabf %O A178803 1,3 %A A178803 _Alford Arnold_, Jun 17 2010