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A122020
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Sum[k=0..n] Eulerian[n,k]*n^k.
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2
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1, 6, 66, 1140, 28280, 948570, 41173776, 2238150600, 148570107264, 11804909261310, 1104566746764800, 120062928157552380, 14986973664751315968, 2127288759957421124610, 340440417300990616995840
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OFFSET
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1,2
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COMMENTS
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n divides a(n). 2^m divides a(n), where m(n) = {0,1,1,2,3,1,4,3,7,1,9,2,10,1,11,4,15,1,17,2,18,1,20,3,22,...}. p^k divides from a(p^k-1), a(p^k), a(p^k+1) for prime p>2 and integer k>0.
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LINKS
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FORMULA
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a(n) = Sum[ Eulerian[n,k]*n^(n-k-1), {k,0,n} ] = n*A122778[n]. a(n) = n(n-1)*A086914[n] for n>1. a(n) = ((n-1)^(n+1)) * PolyLog[ -n, 1/n ] = ((n-1)^(n+1)) * Sum[ k^n/n^k, {k,1,Infinity} ] = ((n-1)^(n+1)) * A121376[n]/A121985[n] for n>1.
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MATHEMATICA
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Table[Sum[Eulerian[n, k]*n^k, {k, 0, n}], {n, 1, 25}]
Flatten[{1, Table[(n-1)^(n+1)*PolyLog[-n, 1/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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STATUS
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approved
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