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A152510
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1/60 of the number of permutations of 5 indistinguishable copies of 1..n with exactly 3 local maxima.
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1
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0, 2, 1066, 328314, 87554515, 22414176982, 5672480870616, 1431066048773744, 360732335571459920, 90911141639422741152, 22910020941551289849856, 5773350885207751422091264, 1454885995214232796339050240, 366631366567387199476086758912, 92391110171365499708617443239936
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OFFSET
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1,2
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LINKS
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FORMULA
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G.f.: x^2*(2 + 302*x - 2858*x^2 - 120673*x^3 - 71148*x^4) / ((1 - 6*x)^3*(1 - 56*x)^2*(1 - 252*x)).
a(n) = 382*a(n-1) - 38020*a(n-2) + 1394280*a(n-3) - 17690400*a(n-4) + 92123136*a(n-5) - 170698752*a(n-6) for n>6.
(End)
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MATHEMATICA
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LinearRecurrence[{382, -38020, 1394280, -17690400, 92123136, -170698752}, {0, 2, 1066, 328314, 87554515, 22414176982}, 20] (* Harvey P. Dale, Mar 14 2022 *)
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PROG
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(PARI) \\ PeaksBySig defined in A334774.
a(n) = {PeaksBySig(vector(n, i, 5), [2])[1]/60} \\ Andrew Howroyd, May 12 2020
(PARI) concat(0, Vec(x^2*(2 + 302*x - 2858*x^2 - 120673*x^3 - 71148*x^4) / ((1 - 6*x)^3*(1 - 56*x)^2*(1 - 252*x)) + O(x^20))) \\ Colin Barker, Jul 19 2020
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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