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A362767
Number of multisets of permutations with a combined total of n moved points spanning an initial interval of positive integers.
2
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
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
KEYWORD
nonn
AUTHOR
Andrew Howroyd, May 04 2023
STATUS
approved