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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, 13507, 15366, 16796, 16796 (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..55. 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 MATHEMATICA T[n_, k_] := T[n, k] = If[n == k, CatalanNumber[n], If[k < 0 || n <= k, 0, T[n-1, k+1] + Sum[T[n-1-i, k-i] CatalanNumber[i], {i, 0, k}]]]; Table[T[n, k], {n, 1, 10}, {k, 0, n-1}] // Flatten (* Jean-François Alcover, Apr 07 2020 *) CROSSREFS Cf. A000108, A001006. Sequence in context: A325260 A325325 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 August 7 17:21 EDT 2024. Contains 375017 sequences. (Running on oeis4.)