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 A322294 Number of permutations of [n] with exactly floor(n/2) rising or falling successions. 4
 1, 1, 2, 4, 10, 48, 120, 888, 2198, 22120, 54304, 685368, 1674468, 25344480, 61736880, 1087931184, 2644978110, 53138966904, 129019925424, 2909014993080, 7056278570108, 176372774697856, 427516982398576, 11729862804913680, 28417031969575260, 848948339328178128 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..696 FORMULA a(n) = A001100(n,floor(n/2)). MAPLE S:= proc(n) option remember; `if`(n<4, [1, 1, 2*t, 4*t+2*t^2]        [n+1], expand((n+1-t)*S(n-1) -(1-t)*(n-2+3*t)*S(n-2)        -(1-t)^2*(n-5+t)*S(n-3) +(1-t)^3*(n-3)*S(n-4)))     end: a:= n-> coeff(S(n), t, floor(n/2)): seq(a(n), n=0..30); MATHEMATICA s[n_] := s[n] = If[n < 4, {1, 1, 2*t, 4*t + 2*t^2}[[n + 1]], Expand[(n + 1 - t)*s[n - 1] - (1 - t)*(n - 2 + 3*t)*s[n - 2] - (1 - t)^2*(n - 5 + t)*s[n - 3] + (1 - t)^3*(n - 3)*s[n - 4]]]; t[n_, k_] := Ceiling[Coefficient[s[n], t, k]]; a[n_] := t[n, Floor[n/2]]; a /@ Range[0, 30] (* Jean-François Alcover, Sep 25 2019, after Alois P. Heinz *) CROSSREFS Bisections give A322295 (even part), A322295 (odd part). Cf. A001100. Sequence in context: A113208 A173488 A000613 * A053500 A214724 A326325 Adjacent sequences:  A322291 A322292 A322293 * A322295 A322296 A322297 KEYWORD nonn AUTHOR Alois P. Heinz, Dec 02 2018 STATUS approved

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Last modified June 25 08:27 EDT 2021. Contains 345453 sequences. (Running on oeis4.)