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 A145224 #22 Aug 29 2024 02:11:27 %S A145224 1,0,1,0,0,1,2,0,0,1,3,8,0,0,1,24,15,20,0,0,1,130,144,45,40,0,0,1,930, %T A145224 910,504,105,70,0,0,1,7413,7440,3640,1344,210,112,0,0,1,66752,66717, %U A145224 33480,10920,3024,378,168,0,0,1 %N A145224 Triangle read by rows: T(n,k) is the number of even permutations (of an n-set) with exactly k fixed points. %H A145224 Bashir Ali and A. Umar, <a href="http://www.seams-bull-math.ynu.edu.cn/downloadfile.jsp?filemenu=_200805&filename=Some Combinatorial Properties of the Alternating Group.pdf">Some combinatorial properties of the alternating group</a>, Southeast Asian Bulletin Math. 32 (2008), 823-830. %F A145224 T(n,k) = C(n,k)*A003221(n-k). %F A145224 E.g.f.: (x^k(1-x^2/2) e^(-x))/k!(1-x). %F A145224 T(n,k) + A145225(n,k) = A008290(n,k). - _R. J. Mathar_, Jul 06 2023 %F A145224 T(n,k) = (A008290(n,k) + A055137(n,k))/2. - _Julian Hatfield Iacoponi_, Aug 08 2024 %e A145224 Triangle starts: %e A145224 1; %e A145224 0, 1; %e A145224 0, 0, 1; %e A145224 2, 0, 0, 1; %e A145224 3, 8, 0, 0, 1; %e A145224 24, 15, 20, 0, 0, 1; %e A145224 ... %Y A145224 Row sums give A001710. %Y A145224 Columns k=0..2 are A003221, A145219, A145220. %Y A145224 Cf. A008290, A055137. %K A145224 nonn,tabl %O A145224 0,7 %A A145224 _Abdullahi Umar_, Oct 09 2008