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A010029 Irregular triangle read by rows: T(n,k) (n>=1, 0 <= k <= floor(n/2)) = number of permutations of 1..n with exactly floor(n/2) - k runs of consecutive pairs up. 2
1, 1, 1, 3, 3, 1, 12, 11, 11, 56, 53, 3, 87, 321, 309, 53, 693, 2175, 2119, 11, 680, 5934, 17008, 16687, 309, 8064, 55674, 150504, 148329, 53, 5805, 96370, 572650, 1485465, 1468457, 2119, 95575 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

REFERENCES

F. N. David, M. G. Kendall and D. E. Barton, Symmetric Function and Allied Tables, Cambridge, 1966, p. 264, Table 7.6.1.

LINKS

Vincenzo Librandi, Rows n = 1..50, flattened

FORMULA

G.f.: Sum_{n>=0}n!*(((1-y)*x^2-x)/((1-y)*x^2-1))^n. - Vladeta Jovovic, Nov 21 2007

EXAMPLE

Triangle begins

     1

     1     1

     3     3

     1    12    11

    11    56    53

     3    87   321    309

    53   693  2175   2119

    11   680  5934  17008   16687

   309  8064 55674 150504  148329

    53  5805 96370 572650 1485465 1468457

  2119 95575 ...

  ...

MATHEMATICA

max = 16; coes = CoefficientList[ Series[ Sum[ n!*(((1 - y)*x^2 - x)/((1 - y)*x^2 - 1))^n, {n, 0, max}], {x, 0, max}, {y, 0, max}], {x, y}]; Table[ Table[ coes[[n, k]] , {k, 1, Floor[(n + 1)/2]}] // Reverse, {n, 2, max - 4}] // Flatten (* Jean-Fran├žois Alcover, Jan 10 2013, after Vladeta Jovovic *)

CROSSREFS

Cf. A000255, A001277, A001278, A001279, A001280.

Sequence in context: A185418 A050609 A120870 * A143603 A094021 A062746

Adjacent sequences:  A010026 A010027 A010028 * A010030 A010031 A010032

KEYWORD

tabf,nonn,nice

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified June 15 08:52 EDT 2021. Contains 345048 sequences. (Running on oeis4.)