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

1,1

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.

Formula

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

Prog

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

Crossrefs

Cf. A018927. Row sums of A299504.

Sequence in context: A259870 A348878 A118100 * A328439 A328504 A279208

Adjacent sequences: A129588 A129589 A129590 * A129592 A129593 A129594

Keyword

nonn

Author

Vladeta Jovovic, May 30 2007

Extensions

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

Status

approved