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 A057740 #35 Jun 14 2024 22:31:10
%S A057740 1,1,1,0,2,1,3,8,1,15,20,0,24,1,45,80,90,144,1,105,350,630,504,210,
%T A057740 720,1,315,1232,3780,1344,5040,5760,0,0,0,0,0,0,0,2688,1,1323,5768,
%U A057740 18900,3024,37800,25920,0,40320,9072,0,15120,0,0,24192
%N A057740 Irregular triangle read by rows: T(n,k) is the number of elements of alternating group A_n having order k, for n >= 1, 1 <= k <= A051593(n).
%D A057740 J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker and R. A. Wilson, ATLAS of Finite Groups. Oxford Univ. Press, 1985 [for best online version see https://oeis.org/wiki/Welcome#Links_to_Other_Sites].
%H A057740 Koda, Tatsuhiko; Sato, Masaki; Takegahara, Yugen; <a href="https://core.ac.uk/download/pdf/59122805.pdf">2-adic properties for the numbers of involutions in the alternating groups</a>, J. Algebra Appl. 14 (2015), no. 4, 1550052 (21 pages).
%H A057740 <a href="/index/Gre#groups">Index entries for sequences related to groups</a>
%e A057740 Triangle begins:
%e A057740 1;
%e A057740 1;
%e A057740 1, 0, 2;
%e A057740 1, 3, 8;
%e A057740 1, 15, 20, 0, 24;
%e A057740 1, 45, 80, 90, 144;
%e A057740 1, 105, 350, 630, 504, 210, 720;
%e A057740 1, 315, 1232, 3780, 1344, 5040, 5760, 0, 0, 0, 0, 0, 0, 0, 2688;
%e A057740 1, 1323, 5768, 18900, 3024, 37800, 25920, 0, 40320, 9072, 0, 15120, 0, 0, 24192;
%e A057740 ...
%t A057740 row[n_] := (orders = PermutationOrder /@ GroupElements[AlternatingGroup[n] ]; Table[Count[orders, k], {k, 1, Max[orders]}]); Table[row[n], {n, 1, 9}] // Flatten (* _Jean-François Alcover_, Aug 31 2016 *)
%o A057740 (Magma) {* Order(g) : g in Alt(6) *};
%Y A057740 Cf. A057731 (S_n), A054522, A057741, A051593, A000793.
%Y A057740 Column 2, 3, 4 are A048099, A001471, A051695.
%Y A057740 See also A061129, A061130, A061131, A061132, A061133, A061134, A061135, A061136, A061137, A061138, A061139, A061140.
%K A057740 nonn,tabf,easy,nice
%O A057740 1,5
%A A057740 _Roger Cuculière_, Oct 29 2000
%E A057740 More terms from _N. J. A. Sloane_, Nov 01 2000
%E A057740 Missing zero in the row for A_9 inserted by _N. J. A. Sloane_, Mar 27 2015