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Row sums of A187783 and A089759.
2

%I #23 Nov 24 2023 05:50:53

%S 1,2,3,5,15,137,4393,518625,239478123,455196345315,4054931519864889,

%T 157048983466046778713,33902817175022723879495899,

%U 33209307490198775518644207834495,202452250996395056747517509528867065999

%N Row sums of A187783 and A089759.

%H Tilman Piesk, <a href="/A248827/b248827.txt">Table of n, a(n) for n = 0..53</a>

%F log(a(n)) ~ n^2 * (log(n/2)/4 + 1/(16*log(n))). - _Vaclav Kotesovec_, Nov 24 2023

%e 1 1

%e 1 1 2

%e 1 1 1 3

%e 1 2 1 1 5

%e 1 6 6 1 1 15

%e 1 24 90 20 1 1 137

%t Table[Sum[((n-k)*k)! / (k!)^(n-k), {k, 0, n}], {n, 0, 15}] (* _Vaclav Kotesovec_, Nov 24 2023 *)

%K nonn

%O 0,2

%A _Tilman Piesk_, Oct 28 2014