A362768 Number of sets of permutations with a combined total of n moved points spanning an initial interval of positive integers.

1, 0, 1, 2, 15, 94, 821, 8012, 91801, 1182490, 17040786, 270878540, 4711273549, 88953035734, 1811836965167, 39594694946864, 924009544908293, 22932616681816514, 603112519409366616, 16753903215777293000, 490184464040864555114, 15066307342227139730694, 485336046152698264379265

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

Cf. A000166, A362767 (multisets).

Sequence in context: A288952 A356554 A356578 * A258390 A027080 A208347

Adjacent sequences: A362765 A362766 A362767 * A362769 A362770 A362771

Keyword

nonn

Author

Andrew Howroyd, May 04 2023

Status

approved