The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A303160 Number of permutations p of [n] such that 0p has exactly ceiling(n/2) alternating runs. 4
 1, 1, 1, 3, 7, 43, 148, 1344, 6171, 74211, 425976, 6384708, 43979902, 789649750, 6346283560, 132789007200, 1219725741715, 29145283614115, 301190499710320, 8092186932120060, 92921064554444490, 2772830282722806978, 35025128774218944648, 1149343084932146388144 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..456 FORMULA a(n) = A186370(n,ceiling(n/2)). EXAMPLE a(2) = 1: 12. a(3) = 3: 132, 231, 321. a(4) = 7: 1243, 1342, 1432, 2341, 2431, 3421, 4321. MAPLE b:= proc(n, k) option remember; `if`(k=0, `if`(n=0, 1, 0), `if`(k<0 or k>n, 0, k*b(n-1, k)+b(n-1, k-1)+(n-k+1)*b(n-1, k-2))) end: a:= n-> b(n, ceil(n/2)): seq(a(n), n=0..25); MATHEMATICA b[n_, k_] := b[n, k] = If[k == 0, If[n == 0, 1, 0], If[k < 0 || k > n, 0, k*b[n-1, k] + b[n-1, k-1] + (n-k+1)*b[n-1, k-2]]]; a[n_] := b[n, Ceiling[n/2]]; Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Aug 31 2021, after Alois P. Heinz *) CROSSREFS Bisections give: A291677 (even part), A303159 (odd part). Cf. A186370. Sequence in context: A101208 A050633 A107636 * A258435 A074268 A019026 Adjacent sequences: A303157 A303158 A303159 * A303161 A303162 A303163 KEYWORD nonn AUTHOR Alois P. Heinz, Apr 19 2018 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified July 12 16:06 EDT 2024. Contains 374251 sequences. (Running on oeis4.)