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A373855
a(n) = Sum_{k=1..n} k! * k^(n-1) * |Stirling1(n,k)|.
4
0, 1, 5, 80, 2690, 155074, 13658386, 1706098008, 286888266696, 62485391828448, 17112247116585744, 5755236604915060944, 2331975856351260982848, 1120439648590390138640304, 629855675998212293917375344, 409557081242059531918330384896
OFFSET
0,3
FORMULA
E.g.f.: Sum_{k>=1} (-log(1 - k*x))^k / k.
MATHEMATICA
nmax=15; Range[0, nmax]!CoefficientList[Series[Sum[(-Log[1 - k*x])^k / k, {k, nmax}], {x, 0, nmax}], x] (* Stefano Spezia, Jun 19 2024 *)
PROG
(PARI) a(n) = sum(k=1, n, k!*k^(n-1)*abs(stirling(n, k, 1)));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jun 19 2024
STATUS
approved