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%I A367012 #12 Dec 31 2023 03:41:44
%S A367012 1,1,2,5,18,95,704,6945,87254,1349603,25064700,548782229,13970248610,
%T A367012 408882114519,13625250384488,512421111644105,21577659567580014,
%U A367012 1010231138742981515,52263989531636074964,2971798406660674944573,184850941269122564302010
%N A367012 a(n) = Sum_{k=0..n} k! * (n-k)^k.
%H A367012 Seiichi Manyama, <a href="/A367012/b367012.txt">Table of n, a(n) for n = 0..315</a>
%F A367012 log(a(n)) ~ n*(2*log(n) - log(log(n)) - 2 - log(2) + log(2*log(n))/(2*log(n)) + 1/(8*log(n)^2)).
%t A367012 Table[Sum[k! * (n-k)^k, {k, 0, n}], {n, 1, 20}]
%o A367012 (PARI) a(n) = sum(k=0, n, k!*(n-k)^k); \\ _Seiichi Manyama_, Dec 31 2023
%Y A367012 Cf. A005193, A026898, A367011.
%K A367012 nonn
%O A367012 0,3
%A A367012 _Vaclav Kotesovec_, Nov 01 2023
%E A367012 a(0)=1 prepended by _Seiichi Manyama_, Dec 31 2023

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