A082426 a(n) = floor(n*n!/2 + 1).

1, 3, 10, 49, 301, 2161, 17641, 161281, 1632961, 18144001, 219542401, 2874009601, 40475635201, 610248038401, 9807557760001, 167382319104001, 3023343138816001, 57621363351552001, 1155628453883904001, 24329020081766400001, 536454892802949120001, 12364008005553684480001

Offset: 1

Author

Benoit Cloitre, Apr 24 2003

Keywords

• nonn
• easy

Comments

Concatenate all the permutations of 1..n in lexicographical order. a(n) is the number of ascending runs. - David Scambler, May 26 2011

Crossrefs

Cf. A074143.

Programs

Maple

seq(floor(n*n!/2 + 1), n=1..20);

Mathematica

a[n_] := Floor[n*n!/2 + 1]; Array[a, 20] (* Amiram Eldar, May 09 2025 *)

PARI

a(n) = (n*n!)\2 + 1; \\ Amiram Eldar, May 09 2025

Formula

a(n) = A074143(n) + 1 for n >= 2. - Georg Fischer, May 15 2024

Extensions

Definition corrected by Georg Fischer, May 15 2024