OFFSET
0,5
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 and p(k)>j for k>j.
FORMULA
O.g.f.: (1-x-I(x))/(1-I(x))^2 where I(x) is the o.g.f. for A003319.
EXAMPLE
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 '.
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]
CROSSREFS
KEYWORD
nonn
AUTHOR
Geoffrey Critzer, Apr 28 2012
STATUS
approved