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A227402
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Number of unimodal functions f:[n]->[n^2].
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4
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1, 1, 16, 525, 24616, 1505205, 113772114, 10253539205, 1073769343504, 128165285630637, 17177527372642000, 2554518029816653175, 417444979902876203656, 74358489250362053975095, 14340040595865309129453250, 2976703788777987140216622005
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) = Sum_{j=0..n^2-1} C(n+2*j-1,2*j), a(0) = 1.
a(n) ~ 2^(n-3/2) * n^(n-1/2) * exp(n+1/4) / sqrt(Pi). - Vaclav Kotesovec, Aug 29 2014
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MAPLE
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a:= n-> `if`(n=0, 1, add(binomial(n+2*j-1, 2*j), j=0..n^2-1)):
seq(a(n), n=0..20);
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MATHEMATICA
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Flatten[{1, Table[Sum[Binomial[n+2*j-1, 2*j], {j, 0, n^2-1}], {n, 1, 20}]}] (* Vaclav Kotesovec, Aug 29 2014 *)
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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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