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 A145224 Triangle read by rows: T(n,k) is the number of even permutations (of an n-set) with exactly k fixed points. 3
 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, 910, 504, 105, 70, 0, 0, 1, 7413, 7440, 3640, 1344, 210, 112, 0, 0, 1, 66752, 66717, 33480, 10920, 3024, 378, 168, 0, 0, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,7 LINKS Table of n, a(n) for n=0..54. Bashir Ali and A. Umar, Some combinatorial properties of the alternating group, Southeast Asian Bulletin Math. 32 (2008), 823-830. FORMULA T(n,k) = C(n,k)*A003221(n-k). E.g.f.: (x^k(1-x^2/2) e^(-x))/k!(1-x). T(n,k) + A145225(n,k) = A008290(n,k). - R. J. Mathar, Jul 06 2023 T(n,k) = (A008290(n,k) + A055137(n,k))/2. - Julian Hatfield Iacoponi, Aug 08 2024 EXAMPLE Triangle starts: 1; 0, 1; 0, 0, 1; 2, 0, 0, 1; 3, 8, 0, 0, 1; 24, 15, 20, 0, 0, 1; ... CROSSREFS Row sums give A001710. Columns k=0..2 are A003221, A145219, A145220. Cf. A008290, A055137. Sequence in context: A373183 A351776 A259784 * A138157 A342243 A073429 Adjacent sequences: A145221 A145222 A145223 * A145225 A145226 A145227 KEYWORD nonn,tabl AUTHOR Abdullahi Umar, Oct 09 2008 STATUS approved

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Last modified September 15 13:15 EDT 2024. Contains 375938 sequences. (Running on oeis4.)