A362768 - OEIS

%I #12 May 06 2023 11:12:50

%S 1,0,1,2,15,94,821,8012,91801,1182490,17040786,270878540,4711273549,

%T 88953035734,1811836965167,39594694946864,924009544908293,

%U 22932616681816514,603112519409366616,16753903215777293000,490184464040864555114,15066307342227139730694,485336046152698264379265

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

%C The permutations in a set are distinct.

%H Andrew Howroyd, <a href="/A362768/b362768.txt">Table of n, a(n) for n = 0..200</a>

%e In the following examples permutations are shown using cycle notation.

%e The a(2) = 1 set of permutations is {(12)}.

%e The a(3) = 2 sets of permutations are {(123)}, {(132)}.

%e 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)}.

%o (PARI) \\ compare with program in A362767.

%o WeighT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v,n,(-1)^(n-1)/n))))-1,-#v)}

%o R(k,n,b)={WeighT(vector(n, j, binomial(k,j)*polcoef(b,j)))}

%o 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)) ))}

%Y Cf. A000166, A362767 (multisets).

%K nonn

%O 0,4

%A _Andrew Howroyd_, May 04 2023