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A288325
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Number of Dyck paths of semilength n such that each positive level has exactly nine peaks.
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2
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1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 440, 6160, 40040, 140140, 280280, 320320, 194480, 48620, 0, 100, 9350, 382800, 9083800, 142638320, 1602400800, 13556342800, 89523519800, 473679520600, 2047398407340, 7334909697400, 22016582387800
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OFFSET
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0,20
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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, 9$2)):
seq(a(n), n=0..42);
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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, 9, 9]];
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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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