A362767 Number of multisets of permutations with a combined total of n moved points spanning an initial interval of positive integers.

1, 0, 1, 2, 16, 94, 836, 8062, 92434, 1187780, 17103983, 271660992, 4722454300, 89127765656, 1814841101699, 39650794527652, 925141689393748, 22957155125457704, 603681013763369997, 16767920412944383544, 490550926763623941996, 15076432260424342403648, 485630804356929583800760

Offset

0,4

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 multiset of permutations is {(12)}.
The a(3) = 2 multisets of permutations are {(123)}, {(132)}.
The a(4) = 16 multisets of permutations are A000166(4) = 9 derangements plus 7 pairs of transpositions which are: {(12), (34)}, {(13), (24)}, {(14), (23)}, {(12), (13)}, {(12), (23)}, {(13), (23)}, {(12), (12)}.

Prog

(PARI) EulerT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, 1/n))))-1, -#v)}
R(k, n, b)={EulerT(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, A362768 (strict case).

Sequence in context: A271273 A220882 A295903 * A141243 A163229 A038749

Adjacent sequences: A362764 A362765 A362766 * A362768 A362769 A362770

Keyword

nonn

Author

Andrew Howroyd, May 04 2023

Status

approved