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 A185652 Number of permutations of [n] having a shortest ascending run of length 2. 3
 0, 0, 1, 0, 5, 18, 89, 519, 3853, 27555, 233431, 2167152, 21596120, 232817282, 2718706924, 33814848445, 448311181346, 6319365554730, 94225534689624, 1481940898130323, 24536143182460549, 426432943716156580, 7762187693343502658, 147704506384475066381 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..150 FORMULA a(n) ~ c * (3*sqrt(3)/(2*Pi))^n * n!, where c = 0.45178068752734823... . - Vaclav Kotesovec, Sep 06 2014 EXAMPLE a(2) = 1: 12. a(4) = 5: 1324, 1423, 2314, 2413, 3412. a(5) = 18: 12435, 12534, 13245, 13425, 13524, 14235, 14523, 15234, 23145, 23415, 23514, 24135, 24513, 25134, 34125, 34512, 35124, 45123. MATHEMATICA A[n_, k_] := A[n, k] = Module[{b}, b[u_, o_, t_] := b[u, o, t] = If[t + o <= k, (u + o)!, Sum[b[u + i - 1, o - i, Min[k, t] + 1], {i, 1, o}] + If[t <= k, u (u + o - 1)!, Sum[b[u - i, o + i - 1, 1], {i, 1, u}]]]; Sum[b[j - 1, n - j, 1], {j, 1, n}]]; a[n_] := A[n, 2] - A[n, 1]; Table[a[n], {n, 0, 23}] (* Jean-François Alcover, Oct 26 2021, after Alois P. Heinz in A064315 *) CROSSREFS Column k=2 of A064315. Cf. A086089 (3*sqrt(3)/(2*Pi)). Sequence in context: A213190 A151490 A282475 * A009305 A097574 A113023 Adjacent sequences: A185649 A185650 A185651 * A185653 A185654 A185655 KEYWORD nonn AUTHOR Alois P. Heinz, Aug 29 2013 STATUS approved

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Last modified May 24 12:09 EDT 2024. Contains 372773 sequences. (Running on oeis4.)