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 A262034 Number of permutations of [n] beginning with at least ceiling(n/2) ascents. 4
 1, 0, 1, 1, 4, 5, 30, 42, 336, 504, 5040, 7920, 95040, 154440, 2162160, 3603600, 57657600, 98017920, 1764322560, 3047466240, 60949324800, 106661318400, 2346549004800, 4151586700800, 99638080819200, 177925144320000, 4626053752320000, 8326896754176000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..733 FORMULA E.g.f.: (exp(x^2)*(x+1)-(x^4/2+x^2+x+1))/x^3. a(n) = 2*((n^2-1)*a(n-2)-a(n-1))/(n+3) for n>3, a(0)=a(2)=a(3)=1, a(1)=0. a(n) = n!/(n/2+1)! if n even, a(n) = floor(C(n+1,(n+1)/2)/(n+3)*((n-1)/2)!) if n odd. a(2n) = A262033(2n) = A001761(n). a(2n+1) = A102693(n+1). Sum_{n>=2} 1/a(n) = (39*exp(1/4)*sqrt(Pi)*erf(1/2) - 6)/16, where erf is the error function. - Amiram Eldar, Dec 04 2022 EXAMPLE a(4) = 4: 1234, 1243, 1342, 2341. a(5) = 5: 12345, 12354, 12453, 13452, 23451. MAPLE a:= proc(n) option remember; `if`(n<4, [1, 0, 1\$2][n+1], 2*((n^2-1)*a(n-2)-a(n-1))/(n+3)) end: seq(a(n), n=0..30); MATHEMATICA np=Rest[With[{nn=30}, CoefficientList[Series[(Exp[x^2](x+1)-x^4/2+x^2+x+1)/ x^3, {x, 0, nn}], x] Range[0, nn]!]//Quiet]; Join[{1}, np] (* Harvey P. Dale, May 18 2019 *) CROSSREFS Cf. A001761, A102693, A262033, A262035. Sequence in context: A041273 A256623 A047169 * A124482 A265709 A265708 Adjacent sequences: A262031 A262032 A262033 * A262035 A262036 A262037 KEYWORD nonn AUTHOR Alois P. Heinz, Sep 08 2015 STATUS approved

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Last modified October 3 09:41 EDT 2023. Contains 365854 sequences. (Running on oeis4.)