OFFSET
0,4
COMMENTS
The permutations in a set are distinct.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..200
EXAMPLE
In the following examples permutations are shown using cycle notation.
The a(2) = 1 set of permutations is {(12)}.
The a(3) = 2 sets of permutations are {(123)}, {(132)}.
The a(4) = 15 sets of permutations are A000166(4) = 9 derangements plus 6 pairs of transpositions which are: {(12), (34)}, {(13), (24)}, {(14), (23)}, {(12), (13)}, {(12), (23)}, {(13), (23)}.
PROG
(PARI) \\ compare with program in A362767.
WeighT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, (-1)^(n-1)/n))))-1, -#v)}
R(k, n, b)={WeighT(vector(n, j, binomial(k, j)*polcoef(b, j)))}
seq(n)={my(b=serlaplace(exp(-x + O(x*x^n))/(1-x))); concat([1], sum(k=1, n, R(k, n, b) * sum(r=k, n, binomial(r, k)*(-1)^(r-k)) ))}
CROSSREFS
KEYWORD
nonn
AUTHOR
Andrew Howroyd, May 04 2023
STATUS
approved