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A229078
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Number of ascending runs in {1,...,n}^n.
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3
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0, 1, 7, 63, 736, 10625, 182736, 3647119, 82837504, 2109289329, 59500000000, 1841557146671, 62041198952448, 2259914256880657, 88499197217837056, 3707501605224609375, 165444235911082541056, 7834451891982365825441, 392371124973096027488256
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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) = n^(n-1)*(n*(n+2)-1)/2 for n>0, a(0) = 0.
E.g.f.: 1/2*W(-x)*(W(-x)^3+W(-x)^2-W(-x)-2)/(1+W(-x))^3, W(x) Lambert's function (principal branch).
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EXAMPLE
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a(1) = 1: [1].
a(2) = 7 = 2+2+1+2: [1,1], [2,1], [1,2], [2,2].
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MAPLE
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a:= n-> `if`(n=0, 0, n^(n-1)*(n*(n+2)-1)/2):
seq(a(n), n=0..25);
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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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