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.

2, 5, 17, 75, 407, 2619, 19487, 164571, 1555007, 16252779, 186167087, 2319025851, 31210884767, 451319283339, 6978220721807, 114883713395931, 2006375649873407, 37048762422505899, 721210940496319727, 14761360406583900411, 316901715602790903647, 7120504270648900589259

Offset: 1

Author

Vladeta Jovovic, May 30 2007

Keywords

• nonn

Comments

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

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..200
• Tanya Khovanova and Daniel A. Klain, What's for dessert?, arXiv:2308.16324 [math.HO], 2023.

Crossrefs

Cf. A018927. Row sums of A299504.

Programs

PARI

a(n)={sum(k=0, n-1, (n-k+1)*k!*((k+1)^(n-k)-k^(n-k)))} \\ Andrew Howroyd, Jan 08 2020

Formula

a(n) = Sum_{k=0..n-1} (n-k+1)*k!*((k+1)^(n-k)-k^(n-k)).

Extensions

Terms a(16) and beyond from Andrew Howroyd, Jan 08 2020