1,2

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.

Eric Weisstein's World of Mathematics, Eulerian number

Eric Weisstein's World of Mathematics, Polylogarithm.

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.

Table[Sum[Eulerian[n, k]*n^k, {k, 0, n}], {n, 1, 25}]

Cf. A122778, A121376, A121985, A086914.

Sequence in context: A090358 A112942 A113390 this_sequence A126459 A054969 A068966

Adjacent sequences: A122017 A122018 A122019 this_sequence A122021 A122022 A122023

nonn

Alexander Adamchuk (alex(AT)kolmogorov.com), Sep 12 2006, Sep 14 2006