A303649 Number of involutions of [n] having exactly one peak.

0, 0, 0, 1, 6, 18, 44, 91, 172, 300, 496, 781, 1186, 1742, 2492, 3479, 4760, 6392, 8448, 11001, 14142, 17962, 22572, 28083, 34628, 42340, 51376, 61893, 74074, 88102, 104188, 122543, 143408, 167024, 193664, 223601, 257142, 294594, 336300, 382603, 433884, 490524

Offset: 0

Author

Alois P. Heinz, Apr 27 2018

Keywords

• nonn
• easy

Examples

			a(3) = 1: 132.
a(4) = 6: 1243, 1324, 1432, 2143, 3412, 4231.
a(5) = 18: 12354, 12435, 12543, 13245, 14325, 14523, 15432, 21354, 21435, 21543, 32154, 34125, 42315, 42513, 45312, 52341, 52431, 53241.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..20000
• Wikipedia, Involution
• Index entries for linear recurrences with constant coefficients, signature (4,-4,-4,10,-4,-4,4,-1)

Crossrefs

Column k=1 of A303648.

Cf. A000085.

Programs

Mathematica

LinearRecurrence[{4,-4,-4,10,-4,-4,4,-1},{0,0,0,1,6,18,44,91},50] (* Harvey P. Dale, Sep 17 2019 *)

Formula

G.f.: x^3*(x^4-2*x^2+2*x+1)/((x+1)^2*(x-1)^6).