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A122778
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Sum_{k=0..n} A(n,k)*n^k where A(n,k) are Eulerian numbers.
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6
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1, 1, 3, 22, 285, 5656, 158095, 5881968, 279768825, 16507789696, 1180490926131, 100415158796800, 10005244013129365, 1152844128057793536, 151949197139815794615, 22696027820066041133056, 3810644613584486281328625
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Prime p divides a(p-1) for p>2. - Alexander Adamchuk, Sep 12 2006
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
| Eric Weisstein's World of Mathematics, Eulerian number at MathWorld
Eric Weisstein's World of Mathematics, Polylogarithm at MathWorld
Digital Library of Mathematical Functions, Table 26.14.1
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FORMULA
| 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..infinity} k^n/n^k for n>1.
a(n) = ((n-1)^(n+1))/n * Li_{-n}(1/n) for n>1. - Alexander Adamchuk, Sep 12 2006
a(n) = (n-1)*A086914(n), n>1. - Vladeta Jovovic (vladeta(AT)eunet.rs), Sep 12 2006
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MAPLE
| 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
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MATHEMATICA
| Table[Sum[Eulerian[n, k]*n^(n-k), {k, 0, n}], {n, 1, 20}] (* Alexander Adamchuk, Sep 12 2006 *)
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CROSSREFS
| Cf. A008292.
Sequence in context: A162659 A206801 A135862 * A108991 A119390 A144681
Adjacent sequences: A122775 A122776 A122777 * A122779 A122780 A122781
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KEYWORD
| nonn
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AUTHOR
| Max Alekseyev (maxale(AT)gmail.com), Sep 11 2006
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EXTENSIONS
| a(0)=1 changed by Max Alekseyev (maxale(AT)gmail.com), Nov 28 2011
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