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A288319
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Number of Dyck paths of semilength n such that each positive level has exactly three peaks.
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2
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1, 0, 0, 1, 0, 0, 0, 4, 20, 20, 0, 16, 200, 1120, 3540, 6864, 9400, 18240, 82000, 364256, 1255040, 3448400, 8094400, 18653984, 50789120, 166596240, 565558400, 1791310496, 5202559520, 14279014880, 39040502400, 111437733184, 335085082880, 1032287357600
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OFFSET
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0,8
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LINKS
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EXAMPLE
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. a(7) = 4:
. /\/\/\ /\/\/\ /\/\/\ /\/\/\
. /\/\/\/ \ /\/\/ \/\ /\/ \/\/\ / \/\/\/\ .
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MAPLE
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b:= proc(n, k, j) option remember;
`if`(n=j, 1, add(b(n-j, k, i)*(binomial(i, k)
*binomial(j-1, i-1-k)), i=1..min(j+k, n-j)))
end:
a:= n-> `if`(n=0, 1, b(n, 3$2)):
seq(a(n), n=0..35);
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MATHEMATICA
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b[n_, k_, j_] := b[n, k, j] = If[n == j, 1, Sum[b[n - j, k, i]*(Binomial[i, k]*Binomial[j - 1, i - 1 - k]), {i, 1, Min[j + k, n - j]}]];
a[n_] := If[n == 0, 1, b[n, 3, 3]];
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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