A316146 - OEIS

%I #16 Nov 22 2021 16:50:23

%S 1,5,67,865,15906,365514,9545026,276368635,9188742238,343857717788,

%T 13998751394662,618098575755637,29469995998980356,1510585321262760900,

%U 83100039017148288635,4873627957977247842223,302388593396139280682588,19804146883678522219587314

%N a(n) = Sum_{k=0..n} Stirling2(n,k) * A000009(k) * k^k.

%H Vaclav Kotesovec, <a href="/A316146/b316146.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(A316145(n) / a(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] * PartitionsQ[k] * k^k, {k, 1, n}], {n, 1, 20}]

%Y Cf. A282190, A305550, A306023, A316145.

%K nonn

%O 1,2

%A _Vaclav Kotesovec_, Jun 25 2018