A330604 a(n) = Sum_{k>=0} (n*k - 1)^n / 2^(k + 1).
1, 0, 9, 278, 16145, 1471774, 194652577, 35275961958, 8397548586177, 2542220603893358, 954003495852753401, 434683708245705663766, 236409592518584290327249, 151286889086525353482149022, 112534788142976814403622739921, 96285847680519841273313314779974
Offset: 0
Keywords
Programs
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Mathematica
Table[Sum[(n k - 1)^n/2^(k + 1), {k, 0, Infinity}], {n, 0, 15}] Join[{1}, Table[n^n HurwitzLerchPhi[1/2, -n, -1/n]/2, {n, 1, 15}]] Table[n! SeriesCoefficient[Exp[-x]/(2 - Exp[n x]), {x, 0, n}], {n, 0, 15}]
Formula
a(n) = n! * [x^n] exp(-x) / (2 - exp(n*x)).
a(n) = Sum_{k=0..n} (-1)^(n - k) * binomial(n,k) * n^k * A000670(k).
a(n) ~ n^n * n! / (2 * (log(2))^(n+1)). - Vaclav Kotesovec, Dec 19 2019