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A129591 For each permutation p of {1,2,...,n} define min(p) = min{ p(i) + i : i = 1..n }; a(n) is the sum of min(p) of all p.

%I A129591 #15 Sep 01 2023 03:57:24
%S A129591 2,5,17,75,407,2619,19487,164571,1555007,16252779,186167087,
%T A129591 2319025851,31210884767,451319283339,6978220721807,114883713395931,
%U A129591 2006375649873407,37048762422505899,721210940496319727,14761360406583900411,316901715602790903647,7120504270648900589259
%N A129591 For each permutation p of {1,2,...,n} define min(p) = min{ p(i) + i : i = 1..n }; a(n) is the sum of min(p) of all p.
%C A129591 a(n) is the number of permutations of [n+1] in which all entries left of 1 (if any) are excedances. An excedance of a permutation p is an entry p(i) such that p(i)>i. For example a(2)=5 counts 123, 132, 213, 231, 312 but not 321 because 2 occurs before 1 yet is not an excedance. - _David Callan_, Dec 14 2021
%H A129591 Andrew Howroyd, <a href="/A129591/b129591.txt">Table of n, a(n) for n = 1..200</a>
%H A129591 Tanya Khovanova and Daniel A. Klain, <a href="https://arxiv.org/abs/2308.16324">What's for dessert?</a>, arXiv:2308.16324 [math.HO], 2023.
%F A129591 a(n) = Sum_{k=0..n-1} (n-k+1)*k!*((k+1)^(n-k)-k^(n-k)).
%o A129591 (PARI) a(n)={sum(k=0, n-1, (n-k+1)*k!*((k+1)^(n-k)-k^(n-k)))} \\ _Andrew Howroyd_, Jan 08 2020
%Y A129591 Cf. A018927. Row sums of A299504.
%K A129591 nonn
%O A129591 1,1
%A A129591 _Vladeta Jovovic_, May 30 2007
%E A129591 Terms a(16) and beyond from _Andrew Howroyd_, Jan 08 2020