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A229003
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Total sum of cubed lengths of ascending runs in all permutations of [n].
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3
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0, 1, 10, 66, 426, 2964, 22818, 195000, 1842234, 19120260, 216604194, 2662063728, 35297775930, 502460232684, 7644691295970, 123824090015544, 2127644969464698, 38659776477571860, 740692592536389474, 14924674961053224000, 315523813278300959994
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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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E.g.f.: (6*exp(x)*(x-1)+x+6)/(x-1)^2.
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MAPLE
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a:= proc(n) option remember; `if`(n<3, [0, 1, 10][n+1],
((2*n^2-3*n-1)*a(n-1) -(n-1)*(n^2-2)*a(n-2)
+(n-2)*(n-1)^2*a(n-3) )/(n-2))
end:
seq(a(n), n=0..25);
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MATHEMATICA
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With[{nn=20}, CoefficientList[Series[(6 Exp[x](x-1)+x+6)/(x-1)^2, {x, 0, nn}], x] Range[ 0, nn]!] (* Harvey P. Dale, Aug 26 2019 *)
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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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