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A235496 a(n) = round(n^n/n!) where round(1/2)=1.

%I A235496 #37 Jan 12 2025 14:56:38
%S A235496 1,1,2,5,11,26,65,163,416,1068,2756,7148,18614,48639,127463,334865,
%T A235496 881658,2325751,6145597,16263866,43099804,114356611,303761260,
%U A235496 807692035,2149632061,5726042115,15264691107,40722913454,108713644516,290404350963,776207020880
%N A235496 a(n) = round(n^n/n!) where round(1/2)=1.
%C A235496 We have two versions of this sequence, this and A240571, because there is no universal agreement on how to round a number like 9/2. - _N. J. A. Sloane_, Dec 13 2015
%H A235496 Vincenzo Librandi, <a href="/A235496/b235496.txt">Table of n, a(n) for n = 0..1000</a>
%F A235496 a(n) = Round(A000312(n)/A000142(n)).
%p A235496 a:= n-> round(n^n/n!):
%p A235496 seq(a(n), n=0..32);  # _Alois P. Heinz_, Dec 13 2015
%t A235496 Table[Floor[n^n/n! + 1/2], {n, 40}]
%o A235496 (Magma) [Round(n^n/Factorial(n)): n in [1..40]];
%o A235496 (PARI) s=[]; for(n=1, 30, s=concat(s, round(n^n/n!))); s \\ _Colin Barker_, Jan 19 2014
%Y A235496 Cf. A000142, A000312, A055775, A073225.
%Y A235496 See A240571 for another version.
%K A235496 nonn,easy
%O A235496 0,3
%A A235496 _Vincenzo Librandi_, Jan 15 2014
%E A235496 Name clarified by _Sean A. Irvine_, Jan 12 2025