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A072285
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Numerators of inverse unimodal analog of binomial coefficients: binomial(n,m) = Sum_{k=0..n-m} a(2*k+m-1, 2*k).
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2
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1, 1, 1, 1, 3, 1, 1, 15, 2, 1, 1, 35, 3, 5, 1, 1, 315, 4, 35, 3, 1, 1, 693, 5, 105, 6, 7, 1, 1, 3003, 6, 1155, 10, 63, 4, 1, 1, 6435, 7, 3003, 15, 231, 10, 9, 1, 1, 109395, 8, 15015, 21, 3003, 20, 99, 5, 1, 1, 230945, 9, 36465, 28, 9009, 35, 429, 15, 11, 1
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OFFSET
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0,5
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LINKS
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FORMULA
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a(n, m) = binomial(n-m/2+1, n-m+1) - binomial(n-m/2, n-m+1).
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MATHEMATICA
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a[n_, m_]:= Binomial[n -m/2 +1, n-m+1] - Binomial[n -m/2, n-m+1]; Flatten[Table[Numerator[a[n, m]], {n, 0, 11}, {m, 0, n}]]
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PROG
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(PARI) a(n, m) = binomial(n-m/2, n-m);
for(n=0, 10, for(m=0, n, print1(numerator(a(n, m)), ", "))) \\ G. C. Greubel, Aug 26 2019
(Sage) [[numerator( binomial(n-m/2, n-m) ) for m in (0..n)] for n in (0..11)] # G. C. Greubel, Aug 26 2019
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CROSSREFS
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KEYWORD
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AUTHOR
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Michele Dondi (bik.mido(AT)tiscalinet.it), Jul 11 2002
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STATUS
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approved
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