A182430 a(n) = n! - A003149(n-1).

1, 0, 0, 1, 8, 56, 408, 3228, 28032, 267264, 2787840, 31662720, 389560320, 5166650880, 73528680960, 1118124000000, 18098712576000, 310759981056000, 5642339254272000, 108022399414272000, 2175029897822208000

Offset: 0

Author

Geoffrey Critzer, Apr 28 2012

Keywords

• nonn

Comments

a(n) is the number of fixed points over all permutations of {1,2,...,n} that are not strong fixed points. Definition by Emeric Deutsch in A003149: a permutation p of {1,2,...,n} is said to have j as a strong fixed point (splitter) if p(k)j for k>j.

Examples

			 a(4)=8 because we have:  1_43'2, 243'1, 32'1_4, 32'41, 413'2, 42'13, 42'3'1.  The permutations are given in one line notation.  The components are separated by _ and the fixed points that are not splitters are marked by '.
		

Crossrefs

Cf. A003149, A003319.

Programs

Mathematica

nn = 20; p = Sum[n! x^n, {n, 0, nn}]; i = 1 - 1/p; CoefficientList[Series[p - x/(1 - i)^2, {x, 0, nn}], x]

Formula

O.g.f.: (1-x-I(x))/(1-I(x))^2 where I(x) is the o.g.f. for A003319.