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A261665 Triangle read by rows: T(n,k) = number of k-classes of permutations of n letters avoiding the pattern 132 (n>=1, 0 <= k <= n-1) 1
1, 2, 2, 4, 5, 5, 9, 12, 14, 14, 21, 30, 37, 42, 42, 51, 76, 99, 118, 132, 132, 127, 196, 265, 331, 387, 429, 429, 323, 512, 714, 922, 1124, 1298, 1430, 1430, 835, 1353, 1934, 2568, 3227, 3872, 4433, 4862, 4862, 2188, 3610, 5268, 7156, 9225, 11384 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

See Baril et al. (2014) for precise definition.

Interpolates between Motzkin numbers (A001006) and Catalan numbers (A000108).

LINKS

Table of n, a(n) for n=1..51.

J.-L. Baril, T. Mansour, A. Petrossian, Equivalence classes of permutations modulo excedances, Journal of Combinatorics, Volume 5 (2014), Number 4, doi:10.4310/JOC.2014.v5.n4.a4. See Table 2.

FORMULA

The proof of Theorem 3.1 in Baril et al. (2014) gives a recurrence for the numbers T(n,k).

EXAMPLE

1

2 2

4 5 5

9 12 14 14

21 30 37 42 42

51 76 99 118 132 132

127 196 265 331 387 429 429

323 512 714 922 1124 1298 1430 1430

835 1353 1934 2568 3227 3872 4433 4862 4862

2188 3610 5268 7156 9225 11384 13507 15366 16796 16796

MAPLE

A261665 := proc(n, k)

    option remember;

    if n = k then

        A000108(n);

    elif k < 0 or n <=k then

        0 ;

    else

        procname(n-1, k+1)+add(procname(n-1-i, k-i)*A000108(i), i=0..k) ;

    end if;

end proc: # R. J. Mathar, Sep 07 2015

CROSSREFS

Cf. A000108, A001006.

Sequence in context: A035632 A114701 A240851 * A208096 A049269 A085085

Adjacent sequences:  A261662 A261663 A261664 * A261666 A261667 A261668

KEYWORD

nonn,tabl

AUTHOR

N. J. A. Sloane, Sep 01 2015

STATUS

approved

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Last modified March 20 15:43 EDT 2019. Contains 321345 sequences. (Running on oeis4.)