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 A287328 Number of permutations of [n] with exactly n (possibly overlapping) occurrences of the generalized pattern 13-2 (alternatively: 2-13, 2-31, or 31-2). 2
 1, 0, 0, 0, 0, 0, 2, 42, 716, 11115, 166144, 2440438, 35573362, 517145226, 7517489564, 109427233994, 1596263948916, 23344423478564, 342325226476816, 5033781463313268, 74223067319020872, 1097343555359525542, 16265399526715750734, 241690082996256941332 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,7 COMMENTS Also number of permutations of [n] with n nestings; also number of permutations of [n] with n crossings. LINKS Alois P. Heinz, Table of n, a(n) for n = 0..300 FORMULA a(n) = A263776(n,n). MAPLE b:= proc(u, o) option remember; `if`(u+o=0, 1, add(b(u-j, o+j-1), j=1..u)+ add(expand(b(u+j-1, o-j)*x^(j-1)), j=1..o)) end: a:= n-> coeff(b(n, 0), x, n): seq(a(n), n=0..30); MATHEMATICA b[u_, o_] := b[u, o] = If[u + o == 0, 1, Sum[b[u - j, o + j - 1], {j, 1, u}] + Sum[Expand[b[u + j - 1, o - j]*x^(j - 1)], {j, 1, o}]]; a[n_] := Coefficient[b[n, 0], x, n]; Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Dec 06 2023, after Alois P. Heinz *) CROSSREFS Main diagonal of A263776. Sequence in context: A140170 A318247 A038396 * A276923 A308526 A162678 Adjacent sequences: A287325 A287326 A287327 * A287329 A287330 A287331 KEYWORD nonn,changed AUTHOR Alois P. Heinz, Aug 31 2017 STATUS approved

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Last modified December 9 13:48 EST 2023. Contains 367691 sequences. (Running on oeis4.)