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A162974 Triangle read by rows: T(n,k) is the number of derangements of {1,2,...,n} having k cycles of length 2 (0 <= k <= floor(n/2)). 0
1, 0, 0, 1, 2, 0, 6, 0, 3, 24, 20, 0, 160, 90, 0, 15, 1140, 504, 210, 0, 8988, 4480, 1260, 0, 105, 80864, 41040, 9072, 2520, 0, 809856, 404460, 100800, 18900, 0, 945, 8907480, 4447520, 1128600, 166320, 34650, 0, 106877320, 53450496, 13347180, 2217600 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Row n has 1 + floor(n/2) entries.

Sum of entries in row n = A000166(n) (the derangement numbers).

T(n,0) = A038205(n).

Sum_{k>=0} k*T(n,k) = A000387(n).

LINKS

Table of n, a(n) for n=0..45.

FORMULA

E.g.f.: G(t,z) = exp(z(tz-z-2)/2)/(1-z).

EXAMPLE

T(4,2)=3 because we have (12)(34), (13)(24), and (14)(23).

Triangle starts:

    1;

    0;

    0,  1;

    2,  0;

    6,  0,  3;

   24, 20,  0;

  160, 90,  0, 15;

MAPLE

G := exp((1/2)*z*(t*z-z-2))/(1-z): Gser := simplify(series(G, z = 0, 16)): for n from 0 to 13 do P[n] := sort(expand(factorial(n)*coeff(Gser, z, n))) end do: for n from 0 to 13 do seq(coeff(P[n], t, j), j = 0 .. floor((1/2)*n)) end do;

CROSSREFS

Cf. A000166, A000387, A038205.

Sequence in context: A076257 A274881 A303638 * A275325 A300227 A290971

Adjacent sequences:  A162971 A162972 A162973 * A162975 A162976 A162977

KEYWORD

nonn,tabf

AUTHOR

Emeric Deutsch, Jul 22 2009

STATUS

approved

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Last modified July 17 16:38 EDT 2019. Contains 325107 sequences. (Running on oeis4.)