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A093768
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Positive first differences of the rows of triangle A088459, which enumerates symmetric Dyck paths.
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5
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1, 1, 1, 1, 2, 3, 1, 3, 8, 6, 1, 4, 15, 20, 20, 1, 5, 24, 45, 75, 50, 1, 6, 35, 84, 189, 210, 175, 1, 7, 48, 140, 392, 588, 784, 490, 1, 8, 63, 216, 720, 1344, 2352, 2352, 1764, 1, 9, 80, 315, 1215, 2700, 5760, 7560, 8820, 5292, 1, 10, 99, 440, 1925, 4950, 12375, 19800
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OFFSET
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0,5
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COMMENTS
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Suggested by Bozydar Dubalski (slawb(AT)atr.bydgoszcz.pl). Related to walks on a square lattice: main diagonal forms A005558, secondary diagonals form A005559, A005560, A005561, A005562, A005563.
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LINKS
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Table of n, a(n) for n=0..62.
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FORMULA
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T(n, k) = C(n+1, ceil(k/2))*C(n, floor(k/2)) - C(n+1, ceil((k-1)/2))*C(n, floor((k-1)/2)) for n>=k>=0.
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PROG
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(PARI) {T(n, k) =binomial(n+1, ceil(k/2))*binomial(n, floor(k/2)) -binomial(n+1, ceil((k-1)/2))*binomial(n, floor((k-1)/2))}
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CROSSREFS
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Cf. A088459, A005558-A005563.
Sequence in context: A100324 A121424 A214978 * A209419 A119011 A130477
Adjacent sequences: A093765 A093766 A093767 * A093769 A093770 A093771
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KEYWORD
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nonn,tabl
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AUTHOR
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Paul D. Hanna, Apr 16 2004
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STATUS
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approved
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