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 A246246 Number of permutations of [n] with exactly one occurrence of the consecutive step pattern up, down, down. 2
 3, 30, 270, 2322, 20772, 195372, 1958337, 20933154, 238789782, 2900868876, 37451986200, 512534035080, 7416327050415, 113185393797510, 1817654015037150, 30647027466113094, 541407973316966604, 10001886705503187732, 192877025408450517501, 3876090406516703418282 (list; graph; refs; listen; history; text; internal format)
 OFFSET 4,1 LINKS Alois P. Heinz and Vaclav Kotesovec, Table of n, a(n) for n = 4..300 (first 160 terms from Alois P. Heinz) FORMULA a(n) ~ c * (3*sqrt(3)/(2*Pi))^n * n! * n, where c = 0.6335500498606750386938465... = c0 * (c0-1)/3, and c0 = (1+exp(Pi/sqrt(3))) * sqrt(3) / (2*Pi). - Vaclav Kotesovec, Aug 22 2014 MAPLE b:= proc(u, o, t) option remember; `if`(u+o=0, 1, expand( add(b(u-j, o+j-1, [1, 3, 1][t])*`if`(t=3, x, 1), j=1..u)+ add(b(u+j-1, o-j, 2), j=1..o))) end: T:= n-> (p-> seq(coeff(p, x, i), i=0..degree(p)))(b(n, 0, 1)): seq([T(n)][2], n=4..20); # Vaclav Kotesovec, Aug 22 2014 after Alois P. Heinz MATHEMATICA b[u_, o_, t_] := b[u, o, t] = If[u + o == 0, 1, Expand[Sum[b[u - j, o + j - 1, {1, 3, 1}[[t]]]*If[t == 3, x, 1], {j, 1, u}] + Sum[b[u + j - 1, o - j, 2], {j, 1, o}]]]; a[n_] := Coefficient[b[n, 0, 1], x, 1]; a /@ Range[4, 20] (* Jean-François Alcover, Dec 28 2020, after Maple *) CROSSREFS Column k=1 of A242819. Sequence in context: A120689 A359614 A180426 * A136896 A121085 A144282 Adjacent sequences: A246243 A246244 A246245 * A246247 A246248 A246249 KEYWORD nonn AUTHOR Alois P. Heinz, Aug 20 2014 STATUS approved

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Last modified December 2 21:21 EST 2023. Contains 367526 sequences. (Running on oeis4.)