A130651 1/16 the number of permutations of 0..n having exactly 3 maxima.

0, 0, 0, 0, 1, 17, 180, 1536, 11616, 81552, 545536, 3532544, 22368000, 139434240, 859634688, 5258379264, 31986270208, 193796182016, 1170829049856, 7059331547136

Offset: 0

Author

R. H. Hardin, Aug 11 2007

Keywords

• nonn

Crossrefs

Cf. A100575.

Formula

Conjecture: a(n) = 2^(n-8)*(3^(n+1) - 2^(n+2)*n + 2*n^2 - 3). - Vaclav Kotesovec, Nov 29 2012

Empirical g.f.: -x^4*(3*x-1) / ((2*x-1)^3*(4*x-1)^2*(6*x-1)). - Colin Barker, Dec 06 2014

Empirical: a(n) = A000487(n+1)/16. - R. J. Mathar, Mar 01 2015