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A122778
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a(n) = Sum_{k=0..n} A(n,k)*n^k where A(n,k) are Eulerian numbers.
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7
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1, 1, 3, 22, 285, 5656, 158095, 5881968, 279768825, 16507789696, 1180490926131, 100415158796800, 10005244013129365, 1152844128057793536, 151949197139815794615, 22696027820066041133056, 3810644613584486281328625
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OFFSET
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0,3
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COMMENTS
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Let A_n(x) denote the Eulerian polynomials with coefficients the Eulerian numbers as defined in the DLMF (number of permutations of {1,2,..,n} with k ascents) then a(n) = A_n(n). - Peter Luschny, Aug 09 2010
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LINKS
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Eric Weisstein's World of Mathematics, Polylogarithm at MathWorld
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FORMULA
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a(n) = Sum_{k=0..n} A(n,k) * n^k
a(n) = Sum_{k=0..n} A(n,k) * n^(n-k).
a(n) = ((n-1)^(n+1))/n * Sum_{k>=1} k^n/n^k for n>1.
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MAPLE
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A122778 := n -> add(n^k*add((-1)^j*binomial(n+1, j)*(k-j+1)^n, j=0..k), k=0..n); # Peter Luschny, Aug 09 2010
seq(add(combinat:-eulerian1(n, k)*n^k, k=0..n), n=0..16); # Peter Luschny, Oct 19 2016
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MATHEMATICA
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<< Combinatorica`; Table[Sum[Combinatorica`Eulerian[n, k] If[n == k == 0, 1, n^k], {k, 0, n}], {n, 0, 20}] (* Alexander Adamchuk, Sep 12 2006; corrected by Vladimir Reshetnikov, Oct 15 2016 *)
Flatten[{1, 1, Table[(n-1)^(n+1)*PolyLog[-n, 1/n]/n, {n, 2, 20}]}] (* Vaclav Kotesovec, Oct 16 2016 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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