%I #16 Nov 22 2021 16:50:44

%S 1,9,106,1823,36821,932080,26666067,876727561,32137538059,

%T 1305168046976,57774609056649,2783202675369037,144453227105110782,

%U 8035192765567735275,476686201707606976317,30053582893540865299197,2005019178999976881804130,141111387620531900621281975

%N a(n) = Sum_{k=0..n} Stirling2(n,k) * A000041(k) * k^k.

%H Vaclav Kotesovec, <a href="/A316145/b316145.txt">Table of n, a(n) for n = 1..370</a>

%F Limit_{n -> infinity} (a(n)/n!)^(1/n) = 1/(log(1+ exp(1)) - 1) = 3.1922192845297391106277924019427161296056687330974482534324... - _Vaclav Kotesovec_, Nov 21 2021

%F log(a(n) / A316146(n)) ~ (sqrt(2) - 1) * Pi * sqrt(n) / sqrt(3*(1 + exp(1)) * log(1 + exp(-1))). - _Vaclav Kotesovec_, Nov 22 2021

%t Table[Sum[StirlingS2[n, k] * PartitionsP[k] * k^k, {k, 1, n}], {n, 1, 20}]

%Y Cf. A167137, A282190, A306022, A316146.

%K nonn

%O 1,2

%A _Vaclav Kotesovec_, Jun 25 2018