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Search: id:A122778
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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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5
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| 0, 1, 3, 22, 285, 5656, 158095, 5881968, 279768825, 16507789696, 1180490926131, 100415158796800, 10005244013129365, 1152844128057793536, 151949197139815794615, 22696027820066041133056, 3810644613584486281328625
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Prime p divides a(p-1) for p>2. - Alexander Adamchuk (alex(AT)kolmogorov.com), Sep 12 2006
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LINKS
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Eric Weisstein's World of Mathematics, Eulerian number at MathWorld
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[ Eulerian[n,k] * n^(n-k), {k,0,n} ]. a(n) = ((n-1)^(n+1))/n * Sum[ k^n/n^k, {k,1,Infinity} ] for n>1. a(n) = ((n-1)^(n+1))/n * PolyLog[ -n, 1/n ] for n>1. - Alexander Adamchuk (alex(AT)kolmogorov.com), Sep 12 2006
a(n) = (n-1)*A086914(n), n>1. - Vladeta Jovovic (vladeta(AT)Eunet.yu), Sep 12 2006
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MATHEMATICA
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Table[Sum[Eulerian[n, k]*n^(n-k), {k, 0, n}], {n, 1, 20}] - Alexander Adamchuk (alex(AT)kolmogorov.com), Sep 12 2006
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CROSSREFS
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Cf. A008292.
Sequence in context: A074706 A141360 A135862 this_sequence A108991 A119390 A124567
Adjacent sequences: A122775 A122776 A122777 this_sequence A122779 A122780 A122781
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KEYWORD
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nonn
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AUTHOR
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Max Alekseyev (maxal(AT)cs.ucsd.edu), Sep 11 2006
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