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A334623
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Sum of the n-th powers of the descent set statistics for permutations of [n].
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4
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1, 1, 2, 18, 1576, 2675100, 128235838496, 265039489112493900, 31306198216486969509375104, 278983981168082455883720325976751040, 235157286166918393786165504356030195355598048512, 23075317400822150539572583950910707053701314350537805923757600
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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) = Sum_{j=0..ceiling(2^(n-1))-1} A060351(n,j)^n.
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MAPLE
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b:= proc(u, o, t) option remember; expand(`if`(u+o=0, 1,
add(b(u-j, o+j-1, t+1)*x^floor(2^(t-1)), j=1..u)+
add(b(u+j-1, o-j, t+1), j=1..o)))
end:
a:= n-> (p-> add(coeff(p, x, i)^n, i=0..degree(p)))(b(n, 0$2)):
seq(a(n), n=0..12);
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MATHEMATICA
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b[u_, o_, t_] := b[u, o, t] = Expand[If[u + o == 0, 1,
Sum[b[u - j, o + j - 1, t + 1]*x^Floor[2^(t - 1)], {j, 1, u}] +
Sum[b[u + j - 1, o - j, t + 1], {j, 1, o}]]];
a[n_] := Function[p, Sum[Coefficient[p, x, i]^n, {i, 0, Exponent[p, x]}]][ b[n, 0, 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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