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 A124774 #10 Sep 17 2024 10:45:23
%S A124774 1,1,1,2,1,3,3,6,1,4,6,12,4,12,12,24,1,5,10,20,10,30,30,60,5,20,30,60,
%T A124774 20,60,60,120,1,6,15,30,20,60,60,120,15,60,90,180,60,180,180,360,6,30,
%U A124774 60,120,60,180,180,360,30,120,180,360,120,360,360,720,1,7,21,42,35,105
%N A124774 Multinomial coefficients for compositions in standard order.
%C A124774 The standard order of compositions is given by A066099.
%C A124774 Number of ways to distribute labeled objects into boxes, with the number of objects in each box being specified by the composition.
%H A124774 Alois P. Heinz, <a href="/A124774/b124774.txt">Rows n = 0..14, flattened</a>
%H A124774 Thomas Garrity and Jacob Lehmann Duke, <a href="https://arxiv.org/abs/2409.05822">Ergodicity and Algebraticity of the Fast and Slow Triangle Maps</a>, arXiv:2409.05822 [math.DS], 2024. See p. 22.
%F A124774 For composition b(1),...,b(k), a(n) = (Sum_{i=1}^k b(i))! / (Product_{i=1}^k b(i)!).
%e A124774 Composition number 11 is 2,1,1; there are 6 choices for the pair of objects in the first box, then 2 choices for the object in the next box, so a(11) = 6*2 = 12.
%e A124774 The table starts:
%e A124774 1
%e A124774 1
%e A124774 1 2
%e A124774 1 3 3 6
%Y A124774 Cf. A066099, A124773, A011782 (row lengths), A000670 (row sums), A036039.
%K A124774 easy,nonn,tabf
%O A124774 0,4
%A A124774 _Franklin T. Adams-Watters_, Nov 06 2006