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A288324
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Number of Dyck paths of semilength n such that each positive level has exactly eight peaks.
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2
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1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 9, 315, 3465, 17325, 45045, 63063, 45045, 12870, 0, 81, 6075, 200340, 3835755, 48617415, 440531784, 3000152925, 15896972520, 67174514550, 230430986514, 649879542063, 1519950287430, 2963421671535, 4828750295985
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OFFSET
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0,18
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LINKS
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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, 8$2)):
seq(a(n), n=0..40);
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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, 8, 8]];
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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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