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A228997
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Total sum of the 7th powers of lengths of ascending runs in all permutations of [n].
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3
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0, 1, 130, 2706, 32226, 315684, 2961498, 28544040, 291590754, 3194874900, 37656861354, 477018980928, 6477756701010, 94006723773564, 1453236561824250, 23855684885059944, 414605141516228418, 7607828522859788580, 147012653519046471114, 2984603478905797978320
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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.: (exp(x)*(42*x^5+210*x^4+280*x^3+126*x-126)+x+126)/(x-1)^2.
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MAPLE
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a:= proc(n) option remember; `if`(n<4, [0, 1, 130, 2706][n+1],
((16*n^3-38*n^2-16*n+278) *a(n-1)
-(8*n^4-3*n^3-101*n^2+623*n-512) *a(n-2)
+2*(n-2)*(8*n^3-32*n^2+134*n-95) *a(n-3)
-(n-2)*(n-3)*(8*n^2-37*n+44) *a(n-4)) /(8*n^2-27*n+24))
end:
seq(a(n), n=0..30);
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MATHEMATICA
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With[{nn=20}, CoefficientList[Series[(Exp[x](42x^5+210x^4+280x^3+126x-126)+x+126)/(x-1)^2, {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Jul 31 2021 *)
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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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