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A300996
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Total sum of half the difference between the area above and the area below the path, measured within the smallest enclosing rectangle based on the x-axis, in all Dyck paths of semilength n.
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2
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0, 0, 0, 1, 6, 28, 122, 516, 2142, 8776, 35630, 143757, 577548, 2313400, 9246556, 36899291, 147073062, 585662952, 2330527172, 9268803248, 36847836764, 146441131058, 581850689938, 2311451765318, 9181309423676, 36466002547328, 144826879361752, 575173217031049
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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) = Sum_{k = -floor((n-1)^2/4)..floor((n-1)^2/4)} k * A300953(n,k).
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EXAMPLE
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a(3) = (1/2) * (0 -2 +2 +2 +0) = 1:
.______.
| /\ |______.______.______.
| / \ | /\/\ | /\ | /\ |______.
|/____\|/____\|/__\/\|/\/__\|/\/\/\|
|9 -9=0|5-7=-2|7 -5=2|7 -5=2|3 -3=0|
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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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