A226998 The number of descents over all functions f:{1,2,...,n}->{1,2,...,n}.

0, 1, 18, 288, 5000, 97200, 2117682, 51380224, 1377495072, 40500000000, 1296871230050, 44952006426624, 1677462128818632, 67068898339975168, 2860906750488281250, 129703669268270284800, 6228632560085359165568, 315864220382241648869376, 16868630748261621128320242

Offset: 1

Author

Geoffrey Critzer, Jun 26 2013

Keywords

• nonn

Comments

A descent is an element j in {1,2,...,n-1} such that f(j) > f(j+1).

Crossrefs

Cf. A225753.

Programs

Mathematica

Table[(n + 1/n -2)*n^n/2,{n,1,20}]

Formula

a(n) = (n + 1/n -2)*n^n/2 = A062023(n) - n^n.