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 A145225 Triangle read by rows: T(n,k) is the number of odd permutations (of an n-set) with exactly k fixed points. 6
 0, 0, 0, 1, 0, 0, 0, 3, 0, 0, 6, 0, 6, 0, 0, 20, 30, 0, 10, 0, 0, 135, 120, 90, 0, 15, 0, 0, 924, 945, 420, 210, 0, 21, 0, 0, 7420, 7392, 3780, 1120, 420, 0, 28, 0, 0, 66744, 66780, 33264, 11340, 2520, 756, 0, 36, 0, 0 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,8 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) * A000387(n-k). E.g.f.: x^(k+2) * exp(-x) / (2*k!*(1-x)). T(n,k) + A145224(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: 0; 0, 0; 1, 0, 0; 0, 3, 0, 0; 6, 0, 6, 0, 0; 20, 30, 0, 10, 0, 0; ... MAPLE A145225 := proc(n, k) binomial(n, k)*A000387(n-k) ; # re-use code of A000387 end proc: seq(seq(A145225(n, k), k=0..n), n=0..12) ; # R. J. Mathar, Jul 06 2023 CROSSREFS Row sums are A001710 for n > 1. Columns k=0..2 are A000387, A145222, A145223. Cf. A008290, A055137. Sequence in context: A062688 A067181 A321429 * A332442 A061480 A220692 Adjacent sequences: A145222 A145223 A145224 * A145226 A145227 A145228 KEYWORD nonn,tabl AUTHOR Abdullahi Umar, Oct 10 2008 STATUS approved

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